I 


WORKS  OF 
PROFESSOR  CECIL  H.  PEABODY 

PUBLISHED    BY 

JOHN  WILEY  &  SONS,  Inc. 


Thermodynamics    of     the  Steam-engine     and 
other  Heat-engines. 

This  work  is  intended  for  the  use  of  students  in 
technical  schools,  and  gives  the  theoretical  training 
required  by  engineers.  Sixth  Edition,  Revised. 
vii+543  pages,  119  figures.  8vo,  cloth,  $4. 50,  net. 
Tables  of  the  Properties  of  Steam  and  other 
Vapors,  and  Temperature-Entropy  Table. 

These  tables  were  prepared  for  the  use  of  students 
in  technical  schools  and  colleges  and  of  engineers  in 
general.  Eighth  Edition,  Rewritten.  8vo,  vi+133 
pages,  cloth,  $1.00,  net. 

Valve-gears  for  Steam-engines. 

This  book  is  intended  to  give  engineering  students 
instruction  in  the  theory  and  practice  of  designing 
valve-gears  for  steam-engines.  Second  Edition, 
Revised  and  Enlarged.  8vo,  v  +142  pages,  33  fold- 
ing-plates, cloth,  $2.25,  net. 
Manual  of  the  Steam-engine  Indicator. 

154  pages,  98  figures.      12mo,  cloth,  $1.50,  net. 
Naval  Architecture. 

Third    Edition,  Revised  and    Enlarged,     vii+641 
pages,  217  figures.     8vo,  cloth,  $7.50,  net. 
Thermodynamics  of  the  Steam  Turbine. 

vi  +282  pages,  103  figures.  8vo,  cloth,  $3.00,  net. 
Propellers. 

iii+132  pages,  29  figures.     8vo,  cloth,  $1.25,  net. 
Computation  for  Marine  Engines. 

8vo,  iv+209  pages,  52  figures.      Cloth,  $2.50,  net. 

BY  PROFESSORS  PEABODY  AND   MILLER 
Steam-boilers. 

By  Prof.  Cecil  H.  Peabody  and  Prof.  Edward  F. 
Miller.  Third  Edition,  Revised  and  Enlarged,  vi  + 
543  pages,  236  figures,  5  folding-plates.  8vo,  cloth, 
$3.75,  net. 


MANUAL 


OF    THE 


STEAM-ENGINE  INDICATOR 


BY 


CECIL    H.    PEABODY, 

Professor  of  Naval  Architecture  and  Marine  Engineering, 
Massachusetts  Institute  of  Technology, 


FIRST   EDITION. 

SECOND   THOUSAND. 


NEW  YORK 

JOHN  WILEY  &  SONS,  INC. 

LONDON:  CHAPMAN  &  HALL,  LIMITED 

1914 


•*A^ 


Copyright,  1900, 

BY 

CECIL  H.  PEABODY. 


THE  SCIENTIFIC   PRESS 
IERT  DRUMMOND   AND   OOMPANV 
BROOKLYN.    N.   Y. 


THE  STEAM-ENGINE  INDICATOR. 


THE  steam-engine  indicator  is  an  instrument  in- 
vented by  Watt  to  measure  and  record  the  pressure 
of  the  steam  in  the  cylinder  of  an  engine.  The  dia- 
grams drawn  by  an  indicator  enable  us  to  calculate 
the  power  of  the  engine,  to  examine  and  adjust  the 
actions  of  the  engine  va'ves,  and  to  make  certain  in- 
ferences concerning  the  transformation  of  heat  into 
work  and  the  influence  of  the  metal  of  the  cylinder 
on  that  operation.  Too  much  emphasis  cannot  be 
given  to  the  fact  that  the  sole  office  of  the  indicator 
is  to  measure  and  record  pressure;  actions  which  are 
commonly  said  to  be  revealed  by  the  indicator  are 
really  inferences  based  on  the  pressure  or  on  changes 
of  pressure. 

The  Watt  Indicator. — While  the  exact  form  of  the 
original  indicator  is  not  known,  it  is  interesting  to 
consider  the  form  ascribed  to  it  by  tradition,  more 
especially  as  that  form  presents  the  elements  of  the 
instrument  clearly.  In  Fig.  i  P  is  a  piston  that  moves 
freely  in  the  cylinder  C,  which  is  open  at  the  top,  and 

359953 


INDICATOR 


can  be  put  in  communication  with  the  interior  of  the 
engine  cylinder  by  the  cock  T  and  a  short  system  of 


FIG.  i. 

piping.  The  piston-rod  HP  passes  up  through  a  hole 
in  the  block  H,  and  carries  a  pencil  p  at  the  upper  end. 
A  helical  spring  between  the  piston  P  and  the  guide- 


THE   STEAM-ENGINE  INDICATOR.  3 

block  H  measures  the  pressure  at  the  under  side  of 
the  piston  P.  At  the  top  of  the  indicator  there  is  a 
light  board  B  which  slides  freely  in  the  frame  EF. 
This  board  has  a  motion  like  that  of  the  piston  of  the 
engine,  on  a  reduced  scale,  which  is  obtained  from  a 
proper  reducing  motion  attached  to  the  crosshead, 
and  is  communicated  by  the  cord  S.  The  weight  W 
on  the  end  of  the  string  S'  pulls  the  board  B  toward 


n 


FIG.  2. 

the  right  and  keeps  the  strings  taut.  A  piece  of  paper 
is  attached  to  the  board  B,  against  which  the  pencil 
p  can  be  pressed  when  a  diagram  is  desired.  Fig.  2 
represents  the  diagram  on  a  larger  scale.  To  take  a 
diagram,  the  string  S  is  connected  to  the  reducing 
motion  so  that  the  board  B  moves  back  and  forth, 
keeping  time  with  the  piston  of  the  engine.  The  cock 
T  is  now  turned  to  open  communication  with  the  en- 
gine cylinder,  and  the  pencil  p  rises  when  steam  is 
admitted  and  falls  when  steam  is  exhausted.  If  the 
engine  runs  slowly  the  pencil  can  be  pressed  against 
the  paper  at  any  position  of  the  piston  of  the  engine; 
for  example,  at  the  beginning  of  the  stroke.  Admis- 


4  THE   STEAM-ENGINE  INDICATOR. 

sion  of  steam  at  the  beginning  of  the  stroke  gives  a 
sudden  rise  of  pressure  represented  by  the  line  AB; 
then  the  piston  of  the  engine  moves  forward  under 
nearly  constant  pressure  of  steam  coming  from  the 
boiler,  until  the  admission  of  steam  is  interrupted  by 
the  closing  of  the  admission-valve;  during  the  re- 
mainder of  the  stroke  of  the  piston  the  steam  in  the 
cylinder  expands  in  volume  and  loses  pressure  as  in- 
dicated by  the  curve  CD;  at  D  the  exhaust-valve 
opens  and  the  pressure  rapidly  falls  to  the  exhaust; 
during  the  greater  part  of  the  return-stroke  of  the 
piston,  steam  is  exhausted  to  the  condenser  at  con- 
stant pressure,  as  represented  by  the  line  EF;  finally 
the  steam  caught  in  the  cylinder  by  the  closure  of  the 
exhaust-valve  is  compressed  as  shown  by  the  curve 
FA.  After  the  diagram  is  completed  the  cock  T  is 
turned  so  as  to  shut  off  communication  with  the  en- 
gine cylinder  and  open  communication  from  the  lower 
end  of  the  cylinder  C,  Fig.  i,  and  the  atmosphere. 
The  pencil  then  comes  to  its  neutral  position  with 
atmospheric  pressure  both  above  and  below  the 
piston  P,  and  with  no  tension  (or  compression)  on 
the  spring.  A  reference-line  //'  is  now  drawn  by  press- 
ing the  pencil  once  again  on  the  paper;  this  is  called 
the  atmospheric  line.  Every  point  of  the  diagram 
corresponds  to  a  definite  position  of  the  engine 
piston;  thus,  n  corresponds  to  one-fourth  stroke  of  the 
piston,  and  further  the  distance  of  n  from  the  line  //' 
measures  the  pressure  of  the  steam  in  the  cylinder  at 


THE  STEAM-ENGINE  INDICATOR.  5 

quarter-stroke,  reckoned  above  the  pressure  of  the 
atmosphere.  During  exhaust,  when  the  steam  is  flow- 
ing into  the  condenser,  the  vacuum  in  the  cylinder  is 
measured  by  the  distance  of  the  pencil  below  the 
atmospheric  line;  the  spring  is  of  course  stretched  in 
tension  while  this  occurs. 

Recent  indicators  differ  from  the  original  proto- 
type in  two  principal  ways:  in  the  first  place,  the 
sliding-board  B  is  replaced  by  a  drum  or  cylinder 
turning  on  a  vertical  axis,  and  in  the  second  place 
the  pencil  is  carried  by  a  parallel  motion  which  multi- 
plies the  motion  of  the  piston.  The  drum  gives  a 
smoother  and  truer  motion  to  the  paper,  and  the  mul- 
tiplication of  the  motion  of  the  piston  by  the  parallel 
motion  permits  of  the  use  of  a  short  and  stiff  spring. 
A  few  well-known  indicators  are  chosen  for  descrip- 
tion; it  will  be  seen  that  they  differ  in  detail  only. 

The  Crosby  Indicator. — Figs.  3  and  4  represent  the 
Crosby  indicator,  made  by  the  Crosby  S'eam-gage 
and  Valve  Company.  Here  8  is  the  piston  of  the 
indicator,  above  which  is  the  spring  which  measures 
the  steam-pressure.  The  motion  of  the  piston  is  mul- 
tiplied by  the  pencil-motion  13,  14,  15,  16,  and  com- 
municated to  the  pencil  23,  which  draws  a  diagram 
on  a  slip  of  paper  that  may  be  wound  around  the 
paper-drum  24. 

The  body  or  barrel  of  this  indicator  is  made  in  three 
pieces,  i,  4,  and  5.  The  part  i  carries  the  paper-drum 
at  the  end  of  an  arm  or  bracket;  the  part  5  has  at  its 


6 


THE   STEAM-ENGINE   INDICATOR. 


lower  end  a  device  for  securing"  the  indicator  to  the 
cock  leading  to  the  engine  cylinder;  the  part  4  is 
bored  out  to  receive  the  piston  8.  The  part  4  is 
more  conveniently  made  separate,  and  may  readily 


FIG.  3. 

be  replaced  if  its  inner  surface  should  become  cut  or 
scored;  it  is  also  surrounded  by  a  steam-jacket,  which 
insures  a  uniform  temperature. 

The  spring,  which  is  shown  separately  by  Fig.  5, 
is  a  double  helix  wound  from  one  piece  of  round  wire, 


THE   STEAM-ENGINE   INDICATOR.  7 

and  screwed  through  the  four  flanges  of  a  brass  head. 
The  length  and  stiffness  of  the  spring  are  adjusted  by 
screwing  it  into  or  out  of  the  head,  and  then  the  wire 


FIG.  4. 

is  secured  by  soldering  it  to  the  head.  The  head  is 
screwed  to  the  cap  2,  Fig.  4,  which  in  turn  is  screwed 
into  the  top  of  the  piece  i.  A  steel  bead  at  the  lower 
end  of  the  spring  affords  the  means  of  connecting 
the  spring  to  the  piston,  as  shown  by  Fig.  4  and 


8 


THE   STEAM-ENGINE  INDICATOR. 


Fig.  6.  The  hub  of  the  piston  is  bored  through  and 
threaded.  A  hollow  piston-rod  is  screwed  down  on 
top  of  the  bead,  and  a  screw  is  screwed  up  from 
below,  and  adjusted  to  take  up  all  looseness  or  back- 
lash without  giving  too  much  pressure  and  friction. 
The  hub  is  slotted  transversely  above  the  piston  to 
allow  the  cross-wire  of  the  spring  to  enter  and  bring 


FIG.  5. 


FIG.  6. 


the  bead  to  the  proper  place.  The  lower  end  of  the 
piston-rod  has  a  lip  which  comes  over  the  ends  of 
the  slotted  hub  and  binds  the  piston-rod  and  hub 
firmly  together. 

The  piston-rod  slides  through  the  cap  2  and  carries 
the  head  n,  which  may  be  screwed  up  or  down  to 
adjust  the  position  of  the  pencil  on  the  paper-drum. 
The  pencil-motion  consists  of  the  pencil-bar  1 6,  which 
is  guided  by  the  link  13,  and  receives  motion  from  the 
piston-rod  head  n,  through  the  transmission-piece 


THE  STEAM-ENGINE  INDICATOR.  9 

14,  which  itself  is  guided  by  the  link  15.  This  forms 
a  kind  of  transformed  grasshopper  parallel-motion, 
so  that  the  pencil  23  moves  on  a  vertical  line  which 
is  very  nearly  straight  within  the  range  of  motion 
allowed,  and  gives  a  close  copy  of  the  motion  of  the 
piston,  but  on  an  enlarged  scale.  The  pencil-motion 
is  carried  by  a  sleeve  3,  which  can  turn  on  the  body 
of  the  indicator,  and  thus  throw  the  pencil  onto  the 
paper-drum,  or  withdraw  it  after  a  diagram  is  taken. 
A  handle  with  a  wooden  knob  and  a  steel  shank  is 
screwed  through  the  wing  x  of  the  sleeve,  and  bears 
against  a  stop  in  the  arm  i,  when  the  pencil  comes  in 
contact  with  the  drum.  The  pressure  of  the  pencil 
against  the  paper-drum  is  adjusted  by  screwing  this 
handle  in  or  out. 

To  assemble  the  piston  and  spring,  etc.,  slack  back 
the  screw  9  in  the  piston  8;  place  the  spring  in  the 
transverse  slot  through  the  top  of  the  hub  of  the 
piston;  screw  down  the  piston-rod  10  firmly  onto 
the  top  of  the  piston-hub,  using  a  socket-wrench  pro- 
vided for  this  purpose;  adjust  the  screw  9  so  that  the 
piston  may  turn  slightly  on  the  'bead  without  friction 
and  without  backlash.  Take  the  sleeve  3  with  pencil- 
motion  attached  in  one  hand  and  the  piston  and 
spring  in  the  other;  catch  the  hollow  piston-rod  into 
the  head  n,  and  then  screw  the  head  of  the  spring 
firmly  onto  the  cap  2.  Slip  the  piston  into  the  cylin- 
der 4,  and  the  sleeve  onto  the  body  of  the  indicator, 
and  screw  down  the  cap  into  place.  Should  the  pen- 


IO  THE  STEAM-ENGINE  INDICATOR. 

cil  be  too  low  down  on  the  paper-drum,  dismount 
the  sleeve  with  the  spring  and  piston,  and  turn  the 
cap  2  toward  the  left,  thus  running  the  head  1 1  further 
out  of  the  piston-rod;  then  replace  the  sleeve  and 
screw  down  the  cap.  Should  the  pencil  be  too  high, 
it  may  be  lowered  in  a  similar  way,  but  the  cap  is  then 
turned  to  the  right  to  run  the  head  1 1  into  the  piston- 
rod. 

The  paper-drum  consists  of  the  thin  shell  24  and 
the  hub  or  body  27.  The  shell  can  be  removed  to  ex- 
pose the  drum-spring  and  other  internal  parts.  The 
hub  turns  on  the  spindle  28,  which  is  screwed  firmly 
into  the  arm  i ;  it  can  turn  through  about  five-sixths 
of  a  rotation  and  is  checked  by  stops.  A  spring  31  is 
clamped  to  the  hub  by  a  plate  32,  and  is  attached  to 
the  spindle  by  a  cap  with  a  square  hole,  resting  on 
a  square  bearing  on  the  spindle.  The  paper-drum 
may  be  turned  in  one  direction  by  drawing  out  the 
cord  which  is  wrapped  around  the  hub,  and  it  is  re- 
turned by  the  drum-spring.  The  cord  may  be  led  in 
any  direction  through  the  fitting  34.  In  the  first 
place,  this  fitting  can  be  revolved  about  a  vertical 
axis  and  clamped  in  place  by  the  milled  head  38;  then 
the  fitting  can  be  rotated  around  a  horizontal  axis 
and  clamped  by  a  milled  head  37;  two  rollers  in  the 
fitting  34  afford  means  of  changing  the  direction  of 
the  cord  at  the  fitting. 

The  Thompson  Indicator. — Fig.  7  shows  the  exter- 
nal appearance  and  Fig.  8  gives  a  vertical  section 


THE   STEAM-ENGINE  INDICATOR.  II 


FIG.  7. 


FIG.  8. 


12 


THE   STEAM-ENGINE   INDICATOR. 


of  the  Thompson  indicator.  It  uses  a  single  helical 
spring  as  shown  by  Fig.  9,  which  is  screwed  onto  the 
piston  at  the  lower  end  and  onto  a  cap  for  the  indica- 
tor-piston at  the  upper  end.  The  pencil-motion  is  a 
modified  grasshopper  parallel  motion  with  the  piston- 


FIG.  9. 


FIG.  10. 

rod  attached  directly  to  the  pencil-bar.  For  com- 
parison we  have  a  diagram  of  an  exact  parallel  motion 
in  Fig.  10,  in  which  it  is  to  be  noted  that  the  guiding- 
link  ab  is  half  the  length  of  the  bar  cp,  and  that  the 
point  p  moves  on  straight  lines  through  a.  The  guid- 
ing-link of  the  pencil-motion  of  the  Thompson 
indicator  is  shortened  and  moved  in  toward  the 
piston-rod,  and  the  pencil  describes  a  slightly  curved 
line;  but  the  deviation  from  a  straight  line  is  scarcely 
perceptible  within  the  range  of  motion  of  the  pencil. 


THE  STEAM-ENGINE  INDICATOR.  13 

The  paper-drum  spring  is  a  flat  spiral  like  a  watch- 
spring.  The  fitting  through  which  the  cord  is  led 
has  one  wheel  instead  of  two,  as  shown  by  Fig.  3  for 
the  Crosby  indicator;  this,  by  the  way,  is  the  original 
form  of  the  fitting,  and  other  forms  are  derived  from 


FIG.  ii. 

it.  The  Thompson  indicator  is  intended  to  be  simple 
and  substantial  so  that  it  may  not  get  out  of  adjust- 
ment if  used  with  ordinary  care. 

The  Tabor  Indictor. — This  indicator  is  represented 
by  Figs,  ii  and  12.  The  most  notable  peculiarity  is 
its  pencil-motion,  which  is  guided  by  a'roller  moving 


14  THE  STEAM-ENGINE   INDICATOR. 

in  a  curved  slot,  as  shown  by  Fig.  12.  The  slot  is 
cut  to  such  a  form  that  the  pencil  is  guided  cor- 
rectly on  a  stra:ght  line,  and  there  is  the  in- 
cidental advantage  that  the  weight  of  the  guid- 
ing-link of  the  pencil-motion  of  the  Thompson  in- 
dicator is  dispensed  with.  But  since  the  roller  must 


FIG.  12. 


be  slightly  smaller  than  the  slot  in  order  that  it 
may  touch  one  side  only,  the  actual  motion  of  the 
pencil  may  deviate  from  a  straight  line,  and  it  is  a 
question  whether  this  pencil-motion  is  appreciably 
better  than  those  which  make  use  of  approximate 
parallel  motions.  A  double  helical  spring  made  of  two 
wires  is  used  in  this  indicator,  as  shown  by  Fig.  13. 
The  cord  from  the  paper-drum  is  led  through  a  disk 


THE   STEAM-ENGINE  INDICATOR.  IS 

with  a  roller,  giving-  the  same  effect  as  the  correspond- 
ing fixtures  of  the  Thompson  and  the  Crosby  indi- 
cators. Fig.  ii  has  a  detent  and  Fig.  12  a  drum-stop 
attachment;  these  details  will  be  considered  later. 

The  Bachelder  Indicator,  shown  by  Figs.  14  and 
15,  has  a  flat  spring  instead  of  the  helical  springs 
used  in  other  indicators.  This  spring,  which  is  shown 


FIG.  13. 

in  full  size  by  Fig.  16,  is  securely  pinned  at  the  farther 
end  and  is  connected  to  the  piston-rod  by  a  pin-joint 
as  shown  in  Fig.  15.  The  effective  length  of  the 
spring  is  the  distance  from  the  piston-rod  to  the  clamp 
a,  Fig.  15,  and  this  length  may  be  changed  by  loosen- 
ing the  screw  at  a  and  sliding  the  clamp  along.  Con- 
sequently the  scale  of  the  spring  can  be  varied 
through  a  wide  range,  and  a  very  few  springs  will 
suffice  for  all  uses  of  the  indicator. 

Indicator    for    Gas-cngincs.  —  Recent    gas-engines 
commonly  have  a  pressure  of  250  or  300  pounds  per 


T6  THE  STEAM-ENGINE  INDICATOR. 


FIG.  14. 


FIG.  15. 


THE  STEAM-ENGINE  INDICATOR.  \f 

square  inch  in  the  cylinder,  generated  by  a  very  rapid 
combustion  or  explosion  of  the  gas  and  air  which 
form  the  working  substance.  Ordinary  steam-en- 
gine indicators,  when  used  on  such  engines,  are  liable 


FIG.  17. 


to  get  out  of  order;  consequently  it  has  been  found 
desirable  to  use  a  special  indicator  for  such  work, 
like  that  shown  by  Fig.  17.  The  piston  has  an  area 
of  one-fourth  of  a  square  inch,  that  is,  half  the  area 


1 8  THE   STEAM-ENGINE  INDICATOR.^ 

of  the  piston  of  a  steam-engine  indicator.  Springs 
supplied  for  steam-engine  indicators  can  be  used 
in  this  instrument  if  rated  at  twice  the  scale  marked 
on  them;  for  example,  a  loo-pound  spring  is  rated 
at  200  pounds,  and  can  be  used  for  a  pressure  of  300 
pounds  to  the  square  inch,  or  more.  The  pencil-bar 
is  made  rigid  to  withstand  the  shock  of  the  explosion 
in  the  gas-engine  cylinder;  extra  weight  in  the  pencil- 
motion  is  of  less  consequence  as  a  stiff  spring  is  al- 
ways used.  The  upper  part  of  the  barrel  is  bored 
out  to  the  usual  diameter  to  accommodate  the  spring, 
which  is  of  the  usual  size  and  form  as  already  pointed 
out.  If  desired,  the  small  piston  shown  in  Fig.  17 
can  be  taken  out  and  a  piston  of  the  pattern  used  for 
steam-engine  indicators,  having  an  area  of  half  a 
square  inch,  can  be  put  in,  and  thus  this  indicator  can 
be  used  for  general  purposes;  but  such  a  use  of  the 
instrument  cannot  be  recommended. 

The  gas-engine  indicator  shown  by  Fig.  17  is  made 
by  the  Crosby  Company,  who  also  make  an  instru- 
ment shown  by  Fig.  18,  which  has  a  piston  or  plunger 
with  an  area  of  1/40  of  a  square  inch.  This  plunger 
bears  on  a  ball-joint  below  a  piston  of  the  ordinary 
size,  above  which  is  the  usual  helical  spring.  Springs 
furnished  for  steam-engine  indicators  must  be  rated 
at  20  times  the  scale  marked  on  them  when  used  with 
this  instrument.  A  side  passage  controlled  by  a  plug- 
valve  may  be  opened  to  give  direct  communication 
with  the  large  cylinder  when  moderate  pressures  are 


THE   STEAM-ENGINE  INDICATOR.  19 

to  be  measured;  but  though  this  may  occasionally  be 
a  convenience  it  is  not  to  be  recommended,  as  the 
side  passage  is  small  and  the  pencil-motion  is  extra 
heavy  to  give  rigidity.  The  post  near  the  paper-drum 


FIG.  18. 

is  intended  to  steady  the  pencil-bar  when  desired. 
This  instrument  is  intended  to  be  used  with  hydraulic 
pumps  and  hydraulic  apparatus,  and  on  pneumatic 
gun-carriages  for  heavy  ordnance.  ~ 

Ammonia  Indicators. — Special  indicators  made  en- 
tirely of  steel  are  supplied  for  indicating  the  compres- 


20 


THE  STEAM-ENGINE  INDICATOR. 


sors    of    ammonia    refrigerating-machines;    for    am- 
monia would  attack  and  soon  destroy  those  parts  of 
a  steam-engine  indicator  that  are  made  of  brass. 
Indicator  Cock. — The  indicator  is  put  in  communi- 


FIG.  19. 


FIG.  20. 

cation  with  the  engine  cylinder  through  a  cock 
and  a  short  system  of  piping  as  shown  by  Fig.  19. 
When  the  handle  is  vertical,  as  shown  by  Fig.  19, 
there  is  a  straight  passage  from  the  cylinder  of  the  en- 
gine to  the  indicator;  but  when  the  handle  is  turned 
down  the  passage  from  the  engine  is  closed,  as  shown 


THE   STEAM-ENGINE  INDICATOR. 


21 


by  Fig.  20,  and  communication  is  opened  to  the  at- 
mosphere through  a  side  passage.  The  cock  is  set  in 
this  last  position  when  the  atmospheric  line  is  drawn. 
Fig.  21  shows  the  elevation  and  Fig.  22  the  section 
of  a  three-way  cock  that  may  be  used  for  taking  dia- 
grams from  both  ends  of  a  cylinder  with  one  indica- 


FlG.    21. 


FIG.  22. 


tor.  A  pipe  from  one  end  of  the  cock  leads  to  the 
head  end  of  the  engine  cylinder,  and  a  pipe  from  the 
other  end  leads  to  the  crank  end  of  the  cylinder;  a 
side  passage  leads  to  the  atmosphere.  Fig.  22  shows 
communication  open  from  one  end  of  the  engine 
cylinder  to  the  indicator;  if  the  handle  is  thrown  to 
the  other  side  the  other  end  of  the  cylinder  will  be  in 
communication  with  the  indicator;  the  indicator  will 
be  open  to  the  atmosphere  when  the  handle  is  in  mid- 
position.  When  convenient  it  is  better  to  use  two  in- 


22  THE  STEAM-ENGINE  INDICATOR. 

dicators  and  avoid  the  considerable  lengths  of  piping 
required  for  a  three-way  cock. 

Inspection  of  the  Instrument. — The  truth  of  a  dia- 
gram taken  by  an  indicator  depends  on  the  construc- 
tion of  the  instrument,  the  condition  in  which  it  is 
maintained,  and  the  skill  with  which  it  is  used. 
Indicators  from  reliable  makers  are  carefully  and 
thoroughly  made  and  are  in  good  condition  when 
sent  out.  An  instrument  which  is  out  of  condition 
from  use  or  accident  should  be  at  once  returned  to 
the  makers  for  repair. 

The  sleeve  which  carries  the  pencil-motion  should 
turn  smoothly  on  the  body  of  the  indicator  and 
be  free  from  looseness  or  backlash.  Friction  at 
this  place  may  be  inconvenient,  but  will  not  af- 
fect the  truth  of  the  diagram;  looseness  will  affect 
the  truth  of  the  diagram  and  should  not  be  tol- 
erated. The  makers  only  can  remedy  defect  in  this 
part.  The  universal  joint  in  the  piston-rod  should 
have  just  enough  freedom  to  avoid  cramping  the 
indicator  piston  in  the  cylinder.  This  joint  for  the 
Crosby  indicator  is  made  on  the  bead  at  the  bot- 
tom of  the  spring  and  must  be  adjusted  when  the 
spring  is  put  in.  The  universal  joint  of  the  Thomp- 
son indicator  is  at  the  middle  of  the  piston-rod  and 
should  be  adjusted  by  the  makers;  a  careful  mecha- 
nician may  be  able  to  .take  up  backlash  due  to  wear 
by  grinding  the  end  of  the  hollow  guiding-rod  which 
runs  through  the  cap,  and  screws  onto  the  lower  half 


THE  STEAM-ENGINE  INDICATOR.  2$ 

of  the  piston-rod.  The  several  joints  of  the  pencil- 
motion  should  be  free  and  without  appreciable  back- 
lash; there  is  no  way  of  detecting  looseness  in  these 
joints  individually,  but  when  the  instrument  is  set 
up  with  a  stiff  spring  in  place,  looseness  in  any  part 
of  the  sleeve,  universal  joint,  or  pencil-motion  will 
appear  if  the  pencil  is  carefully  moved  up  and  down 
with  the  fingers.  If  the  sleeve  and  universal  joint  are 
known  to  be  right  such  looseness  must  be  attributed 
to  the  pencil-motion,  and  will  show  that  the  indica- 
tor must  be  returned  to  the  makers.  Skill  in  detecting 
and  locating  looseness  can  be  acquired  only  by  prac- 
tice. The  pencil-motion  and  sleeve  should  be  oiled 
when  necessary  with  watch-oil. 

The  piston  should  be  a  good,  but  not  a  tight,  fit  in 
the  cylinder  of  the  indicator;  excessive  piston-friction 
will  destroy  the  truth  of  the  diagram;  a  moderate 
leakage  past  the  indicator  does  not  appear  to  have 
much  influence.  The  condition  of  the  piston  and  cyl- 
inder may  be  tested  by  putting  the  indicator  together 
without  a  spring;  in  this  condition  the  piston  should 
fall  freely  from  any  position  when  the  pencil  is  raised 
and  let  fall;  failure  to  fall  freely  indicates  friction 
somewhere.  Excessive  friction  may  occasionally  be 
detected  in  the  pencil-motion  or  in  the  universal  joint 
of  the  piston-rod,  but  usually  such  friction  will  be 
found  at  the  piston.  When  there  is  evidence  of  fric- 
tion the  piston  and  pencil-motion  should  be  removed 
and  both  the  piston  and  the  cylinder  wiped  clean;  this 


24  7W.E   STEAM-ENGINE  INDICATOR. 

may  be  done  with  a  piece  of  clean  cloth  or  with  the 
fingers,  which  should  of  course  be  free  from  grit;  and 
the  piston  should  be  examined  to  detect  roughness 
or  scoring  if  that  has  occurred.  A  slight  roughness 
of  the  piston  or  the  cylinder  can  often  be  reduced  by 
grinding  the  piston  up  and  down  in  the  cylinder,  turn- 
ing it  round  and  round  at  the  same  time.  For  this 
purpose  the  piston  should  simply  be  screwed  onto  the 
piston-rod,  which  can  be  held  in  the  fingers  by  the 
upper  end.  Both  piston  and  cylinder  must  be  wiped 
dry  and  clean  before  beginning  this  process;  emery 
powder  or  other  grinding  material  should  not  be 
used,  the  idea  being  merely  to  rub  down  small  rough- 
nesses. After  the  piston  and  cylinder  are  smooth  and 
clean  the  test  for  freedom  with  the  spring  removed 
should  be  made,  together  with  an  inspection  for  fric- 
tion at  the  joints  of  the  pencil-motion  or  the  universal 
joint.  If  the  piston  and  cylinder  are  so  much  scored 
that  this  process  is  ineffective  it  will  in  general  be  bet- 
ter to  return  the  indicator  to  the  maker;  if  this  cannot 
be  done  the  work  may  be  intrusted  to  a  skilful  me- 
chanic, who  may  grind  the  piston  smooth  in  a  lathe, 
using  fine  emery  or  crocus  paper,  and  afterwards 
grind  the  piston  in  the  cylinder,  using  emery  or 
crocus  powder,  bearing  in  mind  that  the  object  is  to 
remove  the  roughness  due  to  scoring,  and  that  the 
sizes  of  the  piston  and  cylinder  must  not  be  changed. 
Friction  at  the  piston  is  frequently  betrayed  by  the 
diagram,  as  will  be  explained  later,  and  in  such  case 


THE   STEAM-ENGINE  INDICATOR.  2$ 

it  is  usually  sufficient  to  clean  both  piston  and  cylin- 
der and  immediately  put  the  instrument  together 
without  disturbing  the  spring.  When  diagrams  are 
taken  at  intervals  of  five  minutes  or  more  the  indi- 
cator can  be  cleaned  and  adjusted  between  times,  but 
when  diagrams  are  taken  frequently  and  for  some 
considerable  time  it  may  be  advisable  to  have  a  re- 
serve indicator  set  up  and  adjusted  which  may  im- 
mediately replace  the  one  in  use  when  it  shows  signs 
of  clogging  and  consequent  friction. 

The  indicator-piston  may  be  occasionally  oiled  with 
a  little  clean  cylinder-oil;  some  engineers  prefer  to 
use  no  oil,  merely  keeping  the  piston  and  cylinder 
wiped  clean. 

Preparation  for  taking  Diagrams. — When  the  indi- 
cator is  ready  for  use  the  indicator  cock  should  be 
opened  and  blown  through  several  times  to  blow  out 
dirt  and  grit  that  may  be  present.  The  cock  is  then 
closed  and  the  indicator  secured  to  the  cock  and 
adjusted  so  that  the  cord  may  lead  fairly  to  the  reduc- 
ing mechanism.  It  is  very  important  that  the  indi- 
cator shall  be  properly  secured  before  the  steam  is 
let  on  to  take  a  diagram;  failure  to  do  so  may  lead  to 
serious  damage  to  the  instrument,  and  to  delays  and 
annoyances  that  may  be  as  bad.  The  indicator  com- 
monly stands  erect,  but  if  necessary  it  may  be  set 
with  the  paper-drum  horizontal  or  at  an  angle. 

The  cord  leading  from  the  paper-drum  is  now  to  be 
adjusted  to  the  proper  length  to  hook  on  to  the  re- 


26 


THE  STEAM-ENGINE  INDICATOR. 


ducing  mechanism  or  to  a  loop  in  a  cord  tied  to  that 
mechanism.  It  is  convenient  to  tie  the  hook  at  the 
end  of  the  drum  cord  by  a  bowline  knot,  as  shown  by 
Fig.  23,  since  that  knot  is  not  likely  to  slip  and  may 


FIG.  23. 

be  readily  loosened.     Fig.  24  shows  the  same  knot 
partly  tied.    Some  indicator-makers  furnish  a  slip  of 


FIG.  24. 

metal  like  that  represented  by  Fig.  25,  to  facilitate  the 
adjustment  of  the  length  of  the  cord.  The  hook  is 
strung  on  the  loop  at  a.  This  device  gives  added 


FIG.  25. 

weight  at  the  hook  and  will  not  be  found  so  con- 
venient as  a  bowline  knot. 

The  cord  should  always  be  tested  for  length  before 
hooking  onto  the  reducing  motion,  and  must  never 
be  too  short,  as  in  that  case  the  cord  will  be  broken 
or  the  indicator  will  be  injured.  When  the  cord  is 
hooked  on  the  paper-drum  should  run  freely  without 
striking  against  its  stops  at  either  end  of  its  swing. 


THE  STEAM-ENGINE  INDICATOR.  2/ 

On  high-speed  engines  striking  will  be  revealed  by  a 
clicking  noise;  with  a  slow-speed  engine  striking 
may  be  detected  by  holding  the  cord  lightly  in  the 
fingers  and  following  its  motion  without  interfering 
with  the  tension  of  the  drum  spring.  Striking  can 
sometimes  be  detected  from  its  influence  on  the  dia- 
gram, as  will  appear  later. 

There  are  two  ways  in  vogue  of  putting  the  paper 
on  the  paper-drum.  Thus,  the  paper  may  be  taken  by 
its  two  lower  corners  and  looped  over  the  drum,  and 
then  the  end  can  be  drawn  in  succession  under  the 
longer  and  then  the  shorter  of  the  paper-clips. 
The  paper  is  now  drawn  taut  and  true  and  slipped 
down  to  its  place.  Some  prefer  to  fold  and  crease 
one  end  of  the  paper  before  beginning  this  operation. 
Again  the  paper  may  simply  be  wrapped  around  the 
drum,  slipping  one  end  under  both  the  clips,  and  the 
other  over  it  and  under  the  shorter  clip.  The  first 
way  is  more  likely  to  draw  the  paper  snugly  onto  the 
drum,  and  the  second  avoids  the  projecting  edges  of 
the  first  method. 

Paper  and  PendL — Two  kinds  of  paper  are  used  for 
indicator  diagrams,  plain  unprepared  paper  and  a 
paper  which  has  a  special  lead  glaze  which  will  take  a 
mark  from  a  brass  point,  called  metallic  paper.  The 
plain  paper  should  have  a  smooth  surface  with  little 
if  any  glaze,  without  ruling  or  water-marks.  For  such 
plain  paper  a  graphite  pencil  is  used;  it  should  be  of 
the  best  quality  and  of  medium  hardness,  so  that  it 


28  THE   STEAM-ENGINE   INDICATOR. 

will  give  a  fine  clear  line  with  a  light  pressure  on  the 
paper;  its  point  must  be  kept  fine  and  true,  for  a  one- 
sided point  will  spoil  the  geometric  design  of  the 
pencil  motion.  A  short  piece  of  graphite  from  a  cedar 
pencil,  or  a  piece  of  the  graphite  made  for  a  pencil- 
case,  may  'be  used. 

The  metallic  paper  will  usually  be  obtained  from 
the  indicator-maker  cut  to  the  proper  size  for  indicator 
cards,  but  in  some  cases  it  may  be  convenient  to  get 
sheets  of  such  paper  from  dealers  and  cut  it  to  size. 
One  side  of  the  paper  has  a  thick  smooth  glaze,  which 
takes  a  fine  clear  mark  from  a  brass  point.  This 
glaze  is  poisonous,  and  may  even  give  trouble  at  any 
abrasion  of  the  skin  if  handled  freely.  When  metallic 
paper  is  used  the  pencil  will  be  replaced  by  a  brass 
point  furnished  with  the  indicator.  Its  point  should 
be  true  and  fine,  but  not  sharp  enough  to  cut  the 
paper. 

Indicator  Cord. — A  special  braided  cord  is  supplied 
for  indicators,  which  is  of  uniform  size,  strong  and 
comparatively  inelastic;  but  all  fibrous  cord  is  elastic 
and  gradually  stretches  under  tension,  consequently 
the  use  of  long  pieces  of  cord  is  to  be  avoided. 

Drum  Detent. — As  it  is  sometimes  troublesome  to 
hook  the  indicator-drum  cord  onto  the  reducing 
motion,  various  devices  have  been  invented  for  stop- 
ping the  paper-drum  without  unhooking.  At  the  left 
hand  of  the  paper-drum  in  Fig.  1 1  the  rim  of  the  base 
above  the  cord  is  cut  into  ratchet-teeth,  and  there  is 


THE  STEAM-ENGINE  INDICATOR.  2Q 

a  click  on  the  post  that  serves  as  a  stop  for  the  pencil- 
motion,  which  may  engage  these  teeth  when  the 
drum  cord  is  drawn  out.  The  click  may  be  thrown 
forward  to  engage  the  ratchet,  or  may  be  thrown  back 
to  release  the  drum,  and  is  held  in  either  position  by  a 
spring.  To  stop  the  drum,  throw  the  click  forward 
and  draw  the  cord  out  by  hand  till  it  remains  slack. 
The  paper  for  a  diagram  may  then  be  put  on.  To 
release  the  drum,  draw  the  cord  taut  by  hand,  throw 
out  the  click  and  release  the  drum  carefully  so  that 
the  slack  in  the  string  shall  not  be  taken  up  with  a 
jerk  by  the  drum  spring.  The  drum  will  now  move 
with  the  engine  crosshead  and  a  diagram  can  be 
taken. 

Another  way  of  stopping  the  paper-drum  is  shown 
by  Fig.  12.  Here  there  is  a  long  slotted  bar  which  is 
secured  just  under  the  fitting  which  carries  the  guide- 
roller  for  the  cord.  In  the  slot  is  a  sliding  piece  which 
can  be  clamped  anywhere  in  the  slot.  The  upper  end 
of  the  slide  carries  a  second  guide-roller  over  which 
the  cord  passes  on  the  way  from  the  drum  to  the  ad- 
justable guide-fitting.  The  cord  is  given  such  a  length 
that  it  will  rotate  the  paper-drum  properly  when  the 
slide  is  clamped  at  the  outer  end  of  the  slot.  To  stop 
the  drum  the  slide  is  slid  toward  the  inner  end  of  the 
slot,  which  slackens  the  cord  so  that  the  drum  stops. 
An  india-rubber  band  is  tied  on  the  cord  in  such  a  way 
that  it  takes  care  of  the  slack  of  the  cord  while  the 


30  THE   STEAM-ENGINE  INDICATOR. 

drum  is  at  rest;  when  the  cord  is  drawn  taut  the  band 
is  pulled  out  and  lies  along-  the  cord. 

It  will  frequently  be  found  convenient  to  provide 
for  slack  in  a  cord,  or  to  hang  up  the  free  end  of  a 
cord  by  a  rubber  band.  For  this  purpose  a  long 
band  is  required,  strong  enough  to  take  care  of  the 
cord,  but  not  so  stiff  as  to  give  much  additional  ten- 
sion when  the  drum  is  in  motion.  If  a  long  rubber 
band  cannot  be  had,  two  or  three  may  be  united  to 
give  the  proper  length. 

Electrical  Attachment. — When  simultaneous  dia- 
grams are  desired  from  the  several  cylinders  of  a 
compound,  triple-expansion,  or  other  multiple-cylin- 
der engine,  the  electrical  attachment  shown  by  Fig. 
26  will  be  found  convenient.  It  consists  of  an  elec- 
tromagnet M  with  its  armature  A  attached  to  the 
pencil-motion  in  such  a  way  that  the  pencil  is  ap- 
plied to  the  paper  on  the  drum  when  an  electric  cur- 
rent is  passed  through  the  magnet  and  the  armature 
is  drawn  up.  The  magnet  is  carried  by  a  .fixture  S 
which  is  clamped  to  the  body  of  the  indicator  by  the 
screw  E.  CC  are  binding-posts  for  the  wire  from  a 
galvanic  battery,  and  D  is  a  spring  which  holds  the 
armature  in  the  field  of  the  magnet  when  the  circuit 
is  open,  and  throws  back  the  armature  and  removes 
the  pencil  from  the  paper  when  the  current  is  broken. 
All  the  indicators  to  be  operated  are  provided  with 
such  electromagnets  which  are  in  the  same  circuit,  and 
all  can  be  operated  by  closing  the  circuit  by  a  push- 


THE   STEAM-ENGINE  INDICATOR.  3 1 

button  or  otherwise.  Sometimes  one  indicator  is 
worked  by  hand  and  is  provided  with  a  push-button, 
which  is  pushed  up  when  the  pencil-motion  is  forced 
against  its  stop.  The  same  principle  is  used  by 
other  makers  with  various  arrangements  of  details. 


FIG.  26. 

If  an  engine  runs  regu1arly  a  single  operator  can 
take  diagrams  from  the  several  cylinders  in  succes- 
sion by  hand,  just  as  well  as  by  aid  of  the  electrical 
device.  Again,  if  diagrams  are  taken  frequently  it 
will  require  a  number  of  observers  to  keep  the  indi- 
cators working  properly.  It  is  seldom,  if  ever,  that 
the  electrical  device  is  more  than  a  convenience. 


32  THE  STEAM-ENGINE   INDICATOR. 

Reducing  Motions. — Some  form  of  reducing  motion 
is  required  to  give  a  reduced  copy  of  the  motion  of 
the  crosshead  of  the  engine,  and  impart  it  to  the 
paper-drum.  A  few  common  forms  will  be  de- 
scribed; the  engineer  will  have  to  apply  them  to 
special  cases  or  will  have  to  devise  new  ones  as  occa- 
sion may  require.  The  design  for  a  reducing  motion 
should  be  geometrically  correct,  or  else  the  error 
should  be  determined  and  be  kept  within  limit.  In 
general,  the  moving  parts  should  be  light  and  rigid 
and  the  joints  free  from  backlash. 

Brumbo  Pulley. — A  simple  form  of  reducing  mo- 
tion, known  as  a  Brumbo  pulley,  is  shown  by  Fig. 
27.  PN  is  a  vibrating  arm  pivoted  at  P.  The  lower 


3 
C 


FIG.  27. 

end  N  is  connected  by  a  link  NC  with  the  crosshead 
of  the  engine.  The  cord  ,S  from  the  indicator  runs 
on  the  arc  AB.  Usually  the  arc  AB  is  a  circular  arc 
centred  at  the  pivot  P,  and  the  reducing  motion 


THE   STEAM-ENGINE   INDICATOR.  33 

gives  only  an  approximate  copy  of  the  motion  of  the 
crosshead.  This  device  can  be  made  to  give  an  exact 
copy  by  giving  a  correct  form  to  the  arc  AB\  which 
form  must  be  constructed  much  as  a  cam  is  laid  out. 
As  arranged  it  will  commonly  be  found  sufficient  to 
retain  a  circular  ^rc,  but  to  centre  it  at  a  point  a  little 
below  P.  If  more  convenient  the  arc  AB  may  be  in- 
verted and  placed  above  P.  The  cord  may  be  led 
from  the  arc  AB  in  any  convenient  direction,  but  if 
it  is  led  at  an  angle  with  the  horizon  the  arc  AB 
should  be  turned  to  the  same  angle  from  the  vertical. 

This  device  may  be  made  of  wood  if  for  temporary 
use,  or  of  metal  if  permanent.  If  it  is  made  of  wood, 
it  will  be  proper  to  bush  the  bearing  surfaces  at  the 
pins  with  brass;  but  if  made  of  hard  wood,  with  the 
pins  a  tight  fit  in  the  holes,  it  will  run  for  some  time 
without  backlash.  The  bearing  surfaces  at  N  and 
C  should  be  ample  and  the  link  NC  should  be  light, 
especially  when  used  for  a  high-speed  engine.  The 
arm  PN  should  be  rigid  and  the  pivot  free  from 
backlash.  It  is  also  important  that  the  support  for 
the  pivot  shall  be  rigid. 

A  simple  method  of  stopping  the  paper-drum 
without  unhooking  can  be  used  with  this  reducing 
motion.  The  cord  after  passing  over  the  arc  AB  may 
be  led  through  an  eye  at  the  pivot  P.  Adjus:  the 
cord  S  to  the  proper  length  and  tie  a  knot  in  it  just 
before  it  passes  through  the  eye  at  P.  If  the  free  end 
of  the  cord  beyond  the  eye  at  P  is  slackened  the  indi- 


34 


THE   STEAM-ENGINE  INDICATOR. 


cator  drum  will  stop,  and  it  can  be  set  in  motion  by 
drawing  the  free  end  taut  so  that  the  knot  shall  come 
up  to  the  eye.  The  cord  may  be  drawn  up  by  hand 
while  the  diagram  is  taken,  or  it  may  be  drawn  up 
and  hitched  at  some  convenient  point. 

Pantagraph. — A  correct  reducing  motion  may  be 
designed  in  the  form  of  a  pantagraph,  whLh  is  well 


adapted  to  slow-moving  engines;  high-speed  en- 
gines will  quickly  shake  a  pantagraph  to  pieces.  Fig. 
28  shows  a  pantagraph  fixed  to  the  engine-room 
floor,  and  Fig.  29  shows  one  fixed  to  the  frame  of 
the  engine.  The  first  has  adjustable  parts  and  can 
be  used  for  various  engines  as  may  be  found  conven- 
ient; the  second  is  designed  for,  and  used  on,  one 
particular  engine.  The  pantagraph  has  for  its  essen- 
tial part  a  four-bar  cell,  such  as  BEFD,  Fig.  28, 


THE   STEAM-ENGINE  INDICATOR.  35 

which  maintains  the  moving  parts  in  their  proper  re- 
lation. A  point  of  the  pantagraph,  in  this  case  the 
joint  F,  is  pivoted  to  a  fixed  support;  a  point,  as  C, 
on  the  prolongation  of  EB  is  pivoted  to  the  cross- 
head  of  the  engine;  and  a  point,  as  A,  carries  the  in- 
dicator cord.  The  point  A  must  be  on  the  line  CF 
through  the  moving  point  C  and  the  fixed  point  F, 
and  must  divide  it  so  that  AF  is  to  CF  as  the  length 
of  the  diagram  is  to  the  stroke  of  the  engine.  The 
cord  AP  must  be  led  off  parallel  to  the  motion  of 
the  crosshead;  if  necessary  the  cord  may  be  led 
round  a  guide-wheel,  as  at  P,  on  the  way  to  the  indi- 
cator. To  make  this  pantagraph  adjustable  a  series 
of  holes  is  provided  for  the  pivot  C,  and  the  bar  BD 
can  be  set  at  various  distances  from  FE;  the  point  A 
is  sometimes  carried  by  an  adjustable  sliding  piece 
that  can  be  clamped  to  the  bar  BD,  but  more  com- 
monly the  adjustment  is  made  by  providing  a  series 
of  holes  for  a  pin  that  can  be  screwed  into  the  bar 
BD.  In  this  latter  case  the  point  A  will  not  always 
be  exactly  on  the  line  CF,  but  a  slight  deviation  will 
have  little  effect.  This  pantagraph  can  be  made  of 
metal,  or  of  wood  bushed  with  brass,  or  of  wood  with 
metallic  pins  only  if  the  latter  are  a  tight  fit  for  the 
holes. 

In  laying  out  a  pantagraph  for  a  particular  engine 
as  represented  by  Fig.  29,  we  may  proceed  as  fol- 
lows. In  the  first  place  AI  is  to  be  drawn  at  the 
proper  height  to  lead  correctly  from  the  indicators; 


$6  THE   STEAM-ENGINE   INDICATOR. 

it  may  be  a  piece  of  indicator  cord  or  it  may  be  a 
rod  sliding  in  guides  at  the  end  /.  The  line  FC  is 
to  be  made  of  a  proper  length  to  avoid  awkward  po- 
sitions of  the  pantagraph  when  the  crosshead  is  at 
the  ends  of  the  stroke;  it  will  be  well  to  limit  the 
total  angular  motion  of  the  line  FC  (from  side  to 
side)  to  60°.  The  line  FC  will  now  be  divided  at  A 
so  as  to  give  the  proper  length  to  the  indicator  dia- 
gram. Ordinarily  the  points  F  and  C  will  have  to 
be  located,  one  on  a  post  on  the  engine  frame  and 
the  other  on  an  arm  projecting  downward  from  the 
crosshead.  The  bars  FE,  EC,  HK,  and  HG  must  be 
drawn  ir  by  trial  to  give  a  convenient  arrangement 
of  joints  and  other  details.  This  pantagraph  will  be 
preferably  made  of  metal  throughout.  If  the  joints 
wear  loose  the  holes  may  be  rebored  and  fitted  with 
larger  pins.  When  applied  to  a  vertical  engine  the 
mechanism  will  be  turned  through  a  right  angle  so 
that  I A  will  be  vertical. 

A  modification  of  the  pantagraph,  known  as  the 
lazy-tongs,  is  shown  by  Fig.  30.  The  joint  B  is 
pivoted  to  a  convenient  fixture  near  the  engine,  and 
the  pin  A  is  slipped  into  a  ho1e  in  the  crosshead  or 
in  a  piece  which  is  fastened  to  it.  The  indicator  cord 
is  led  from  the  pin  E  parallel  to  the  motion  of  the 
crosshead.  The  bar  DC  is  set  so  as  to  give  the  proper 
length  of  diagram,  and  the  pin  E  is  set  on  a  line  from 
A  to  B.  The  lazy-tongs  is  commonly  made  of  wood 
and  has  considerable  flexibility,  which,  with  the  large 


THE   S7*EAM-ENGINE   INDICATOR. 


37 


number  of  joints  to  get  loose,  makes  it  rather  a  crude 

device. 

A 


FIG.  30. 

Swinging-lever  and  Slider. — A  simple  and  service- 
able reducing  motion  is  shown  by  Fig.  31.     It  con- 


sists of  a  swinging-lever  AB  which  is  connected  to 
the   crosshead   by   a   link  BC\   a   parallel    link   ED 


38  THE  STEAM-ENGTNE  INDICATOR. 

moves  a  sliding-rod  DF,  which  moves  in  guides  par- 
allel to  the  motion  of  the  crosshead.  The  point  D 
is  on  the  line  AC,  and  divides  it  so  that  AD  is  to  AC 
as  the  length  of  the  diagram  is  to  the  stroke  of  the 
engine.  The  rod  DF  is  made  long  enough  to  reach 
to  the  indicator,  which  can  be  hooked  directly  onto 
a  pin  set  in  the  rod  for  that  purpose.  The  links  may 
be  made  double  or  may  have  forked  ends  at  D,  E, 
and  B. 

Reducing-whcel. — A  portable  reducing  motion  is 
shown  attached  to  an  indicator  in  Fig.  32.  The  in- 
dicator cord  is  wound  round  a  drum  A  which  can 
turn  on  a  vertical  post  or  spindle,  and  which  is  kept 
wound  up  by  a  clock-spring  in  its  base.  The  wheel 
B  is  geared  to  the  drum  by  spur  gears  (not  shown 
in  the  figure)  so  that  it  makes  three  turns  for  one 
turn  of  the  drum  A.  A  long  cord  is  wound  in  a 
helical  groove  on  the  wheel  B  and  is  led  directly  to 
the  crosshead  of  the  engine.  The  wheel  turns  on  a 
screw-thread  cut  on  its  spindle,  so  that  it  descends  as 
the  cord  is  drawn  out  and  rises  as  the  cord  is  wound 
up,  and  the  cord  is  consequently  wound  truly  in  the 
helical  groove.  The  drum  A  may  be  varied  in  size 
to  conform  to  the  stroke  of  the  engine;  a  small  drum 
is  used  for  a  long-stroke  engine  and  vice  versa.  Since 
the  wheel  B  turns  rapidly  and  must  start  and  stop 
with  the  crosshead,  it  is  made  of  aluminium  for  sake 
of  lightness. 

ig.  33  shows  a  form  of  reducing  motion  which 


THE   STEAM-ENGINE  INDICATOR 


39 


has  a  cord  from  the  engine  crosshead  wound  on  the 
wheel  0,  and  which  drives  the  paper-drum  by  a 
worm  gear  R.  Several  sizes  of  wheels  are  supplied 


to  conform  to  the  stroke  of  the  engine.  A  spring 
for  winding  up  the  cord  is  contained  in  the  case  d. 
At  u  is  a  milled  head  which  controls  a  clutch  on 
the  wheel-shaft.  When  this  clutch  is  released  the 


40 


THE  STEAM-ENGINE  INDICATOR. 


wheel  turns  freely  on  its  shaft  and  the  paper-drum 
remains  at  rest  against  one  of  its  stops.  When  the 
clutch  is  thrown  into  gear  the  wheel  is  clamped  to 
its  shaft,  which  now  drives  the  paper-drum  by  aid 
of  the  worm  gear.  To  start  the  paper-drum,  turn  it 


FIG.  33. 

forward  by  the  milled  head  above  it,  so  that  it  stands 
at  least  a  quarter  of  an  inch  free  from  its  stop,  and 
throw  in  the  clutch  at  u.  It  may  be  released  by 
throwing  out  the  clutch. 

Wire  instead  of  Cord. — On  large  engines  the  indi- 
cators are  at  a  considerable  distance  from  the  cross- 


THE  STEAM-ENGINE   INDICATOR.  41 

head  and  the  reducing  motion.  It  is  sometimes 
recommended  to  use  wire  to  transfer  the  motion  to 
the  indicator,  and  this  may  be  of  service  with  slow 
engines,  especially  if  the  wire  can  be  kept  taut  by  a 
weight  or  spring.  On  high-speed  engines  the  wire 
is  likely  to  sway  from  side  to  side  and  give  more 
trouble  than  cord.  Properly  the  motion  should  be 
transferred  by  a  sliding  rod  used  in  connection  with 
a  correct  and  rigid  reducing  motion. 

Taking  Diagrams. — When  the  indicator  is  ready 
and  a  diagram  is  desired,  start  the  paper-drum  by 
hooking  on  the  cord  or  by  aid  of  the  starting  device 
when  one  is  provided,  and  turn  on  the  steam;  let 
the  indicator  move  idly  until  it  is  hot  and  clear  of 
water;  press  the  pencil-motion  against  its  stop  until 
a  complete  diagram  is  drawn;  shut  off  the  steam 
from  the  indicator  and  again  press  the  pencil-motion 
against  the  stop  to  draw  the  atmospheric  line;  stop 
the  paper-drum  and  remove  the  diagram  and  num- 
ber or  otherwise  identify  it.  If  other  diagrams  are 
to  be  taken  it  is  well  to  place  another  paper  on  the 
drum. 

The  atmospheric  line  must  be  taken  after  the  in- 
dicator is  hot;  it  will  be  wrongly  located  if  drawn 
when  the  instrument  is  cold.  The  instruction  to 
draw  the  atmospheric  line  after  the  diagram  is  taken 
is  for  this  purpose.  If  the  engine  runs  slowly  the 
pencil  may  be  applied  during  exhaust,  because  this  is 
a  long  line  which  is  little  liable  to  change,  and  thus 


42  THE   STEAM-ENGINE  INDICATOR. 

a  single  complete  diagram  can  be  drawn.  If  the  en- 
gine runs  rapidly  such  refinement  is  impossible,  and 
it  will  be  sufficient  to  hold  the  pencil-motion  against 
the  stop  for  a  revolution  of  the  engine  as  nearly  as 
may  be.  In  indicating  high-speed  engines  it  will 
be  found  that  two  or  more  diagrams  are  super- 
imposed even  though  the  pencil  is  applied  to  the 
paper  for  an  instant  only;  but  as  the  diagrams 
usually  change  little  if  at  all  no  inconvenience  will 
result.  Some  engineers  prefer  to  get  several  super- 
imposed diagrams  and  thus  get  a  rough  average. 
For  important  work  it  is  essential  that  the  engine 
shall  run  regularly,  and  then  the  diagrams  will  re- 
main constant  or  change  slowly. 

Care  of  the  Instrument. — After  all  the  diagrams  de- 
sired are  taken,  the  indicator  is  to  be  removed  from 
the  engine,  cleaned  and  dried,  oiled  and  put  in  its 
case.  In  taking  the  indicator  from  the  engine  the 
hands  should  be  protected  to  avoid  burning  them, 
and  consequent  danger  of  dropping  the  instrument 
or  some  part  of  it.  If  the  indicator  is  taken  apart 
while  hot  and  the  several  pieces  cleared  from  water 
as  well  as  may  be,  and  allowed  to  lie  exposed  to  the 
air,  they  will  dry  off  so  that  they  may  be  readily 
cleaned  and  wiped  dry.  The  spring  and  other  parts 
that  are  made  of  steel  should  be  oiled  to  guard 
against  rust. 

Scale  of  Spring. — The  spring  used  should  be 
chosen  with  reference  to  the  highest  expected  pres- 


THE   STEAM-ENGINE    INDICATOR.  43 

sure;  the  height  of  the  diagram  should  not  exceed 
if  to  2  inches.  If  the  diagram  lies  entirely  above 
(or  below)  the  atmospheric  line  this  height  is  to  be 
measured  from  that  line;  if  partly  above  and  partly 
below  the  height  is  that  of  the  diagram  itself.  In 
general,  the  use  of  a  spring  weaker  than  20  pounds 
to  the  inch  should  be  avoided,  and  for  high-speed  en- 
gines it  is  well  to  use  a  4O-pound  spring  or  even  a 
siiffer  one.  A  small  clear  diagram  is  to  be  preferred 
to  a  large  irregular  one. 

Indicator  Diagram. — Fig.  34  may  be  taken  to  rep- 
resent a  typical  diagram  from  a  non-condensing  en- 


FIG.  34. 

gine.  Steam  is  admitted  to  the  cylinder  when  the 
piston  has  nearly  reached  the  end  of  its  stroke,  due 
to  the  lead  of  the  steam-valve,  as  represented  by  the 
line  fa,  which  inclines  toward  the  left  in  the  figure. 
From  a  to  b  is  the  steam-line  which  is  drawn  by  the 
indicator  while  steam  is  admitted  to  the  cylinder,  and 
d  represents  the  cut-off  or  closure  of  the  steam-valve. 
After  cut-off  the  steam  expands  with  increase  of  vol- 


44 


THE   STEAM-ENGINE  INDICATOR. 


ume  and  fall  of  pressure,  as  represented  by  the  ex- 
pansion-line be,  until  the  exhaust-valve  opens  at  c. 
From  release  at  c  to  the  end  of  the  stroke  there  is  a 
rapid  fall  of  pressure,  represented  by  cd.  During  the 
return-stroke  steam  is  forced  out  of  the  cylinder 
against  the  pressure  of  the  atmosphere,  as  repre- 
sented by  de  (which  is  called  the  back-pressure  line) 
until  the  exhaust-valve  closes  at  e.  From  e  to  f  steam 
is  compressed  ahead  of  the  piston  with  diminution  of 
volume  and  rise  of  pressure.  The  atmospheric  line 
is  represented  by  mn. 

A  diagram  like  Fig.  34  with  straight  lines  and 
sharp  corners  is  never  obtained  in  practice,  for  valves 
do  not  open  and  close  instantly  and  the  indicator  has 


(*  ft  * 


FIG.  35. 

a  tendency  to  run  one  line  into  another.  The  actual 
diagram  is  more  like  Fig.  35,  which  shows  some  loss 
of  pressure  during  the  admission  of  steam  from  a  to 
X^  and  a  rounded  corner  at  cut-off.  The  release  cd 
is  shown  with  a  convex  curve  outward,  as  is  usually 
found  with  quick-running  engines.  Finally  efa  ap- 
pears as  a  continuous  curve  without  corners  and 


THE  STEAM-ENGINE  INDICATOR.  45 

without  a  well-defined  separation  of  compression  (ef) 
from  admission  (fa). 

Summing  up  we  have 

ab,  steam-line.  o,  initial  pressure. 

be,  expansion-line.  b,  cut-off. 

cd,  release.  c,  release. 

de,  back-pressure  line.        e,  compression. 
ef,  compression.  f,  admission. 

fa,  admission. 

Fig.  35  is  drawn  with  a  scale  of  60  pounds  to 
the  inch,  and  the  point  a  is  one  inch  from  the 
atmospheric  line  and  represents  a  pressure  of  60 
pounds  to  the  square  inch  initial  pressure  above  the 
atmosphere.  Or  more  conveniently,  if  the  distance 
of  a  from  mn  is  measured  by  a  scale  divided  into 
6oths  of  an  inch,  it  will  be  found  at  the  6oth  division 
of  the  scale.  In  the  same  way  the  pressure  of  release 
is  found  by  a  scale  of  6oths  (called  a  60  scale)  to  be 
1 8  pounds  above  the  atmosphere,  while  the  back- 
pressure is  found  to  be  about  one  pound  above  the 
atmosphere. 

The  location  of  the  point  of  cut-off  and  the  point 
of  release  is  always  somewhat  uncertain  on  account 
of  the  rounding  of  the  corners  already  spoken  of.  It  is 
customary  to  consider  that  the  cut-off  is  at  the  point 
b,  Fig.  36,  when  the  convex  rounding  of  the  corner 
due  to  the  closing  of  the  steam-valve  changes  into  the 
concave  expansion-curve  be.  Release  is  assumed  to 
take  place  at  c  where  the  expansion-curve  runs  into 


46 


THE   STEAM-ENGINE  INDICATOR. 


the  release  line  cd.  Compression  is  located  at  e  where 
the  pressure  begins  to  rise  above  the  back-pressure 
line.  To  determine  the  per  cent  of  the  stroke  at 
which  cut-off,  release,  and  compression  occur  draw 
lines  ma  and  nd  perpendicular  to  the  atmospheric 
line  mn  and  just  touching  the  diagram  at  its  ends; 


FIG.  36. 

also  draw  vertical  lines  at  b,  c,  and  e,  the  points  of 
cut-off,  release,  and  compression;  select  a  scale  such 
that  100  divisions  on  it  shall  be  a  little  longer  than 
the  diagram,  and  lay  it  diagonally  across  the  diagram 
so  that  the  zero  shall  be  on  the  line  ma  and  the  di- 
vision 100  on  the  line  nd\  the  per  cents  may  now  be 
read  directly  from  the  scale — for  example,  cut-off  is 
at  29  per  cent,  release  is  at  83  per  cent,  and  com- 
pression is  at  22  per  cent  of  the  stroke. 

Errors  of  the  Indicator. — The   steam-engine  indi- 
cator is  the  engineer's  main  reliance  in  investigations 


THE   STEAM-ENGINE   INDICATOR.  47 

of  the  performance  of  steam-engines,  and  its  indica- 
tions are  commonly  accepted  implicitly  by  the  en- 
gineer who  seldom  has  the  time  or  the  means  of 
properly  standardizing  his  indicators.  Unfortunately 
the  indicator  is  subject  to  errors  which  are  neither 
small  nor  well  known,  even  though  indicator-makers 
have  given  much  thought  and  skill  to  the  perfecting 
of  their  instruments,  and  though  much  time  has  been 
given  by  engineers  to  experimental  investigations  of 
the  errors  of  indicators. 

There  are  two  ways  of  considering  the  errors  of 
indicators:  firstly,  the  errors  may  be  analyzed  to  the 
end  that  imperfections  may  be  located  and  the  proper 
remedies  may  be  sought;  and  secondly,  the  actual 
error  of  the  instrument  in  service  may  be  investi- 
gated in  order  that  the  proper  estimate  may  be  at- 
tributed to  its  indications. 

In  the  first  place  the  errors  of  the  pencil-motion 
piston  and  attached  parts  may  be  considered  sepa- 
rately from  those  of  the  paper-drum.  The  latter  will 
be  considered  first  as  they  are  comparatively  simple 
and  may  be  almost  entirely  eliminated  by  using 
proper  reducing  motions. 

Errors  of  Paper-drum. — It  is  apparent  that  if  the 
paper  or  card  could  have  a  positive  motion  given  to 
it  by  a  correct  indicator-motion,  it  would  give  an 
exact  reproduction  of  the  motion  of  the  engine  cross- 
head  and  there  would  be  no  paper-drum  errors.  If 
necessary  the  card  could  be  carried  by  a  proper  flat 


48  THE   STEAM-ENGINE   INDICATOR. 

board  on  the  slide  FD  of  Fig.  31,  page  37;  or  a  posi- 
tive connection  from  such  a  slide  to  the  paper-drum 
could  be  devised.  The  entire  error  of  the  paper- 
drum  is  to  be  attributed  to  the  cord  and  spring  by 
which  the  drum  is  drawn  out  and  returned. 

There  are  three  sources  of  error  of  the  paper-drum 
that  can  be  identified,  namely,  the  paper-drum 
spring,  the  inertia  of  the  drum,  and  the  friction  of  the 
drum. 

Paper-drum  Spring. — A  long  flat  spiral  spring  like 
a  clock  spring  is  used  by  some  makers  for  returning 
the  paper-drum;  others  use  a  helical  spring,  as  shown 
by  Fig.  4,  page  7.  The  first  form  is  intended  to  give 
a  uniform  tension  on  the  cord,  and  the  second  form 
is  intended  to  give  an  increasing  tension  as  the  cord 
is  drawn  out.  Both  give  increasing  tension,  though 
the  increase  due  to  a  flat  spiral  spring  may  be  the 
smaller.  The  increase  of  tension  lengthens  the  cord, 
and  the  diagram  is  shortened  to  just  that  extent.  As 
the  cord  is  uniform  in  strength  and  elasticity  the  re- 
duction in  the  length  of  the  diagram  is  evenly  dis- 
tributed and  the  truth  of  the  diagram  is  but  little 
affected.  This  effect  is  found  in  indicating  an  engine 
at  slow  speed  when  a  long  cord  is  used.  On  high- 
speed engines  this  effect  is  obscured  by  the  influence 
of  the  inertia  of  the  paper-drum. 

Inertia  of  the  Paper-drum. — At  the  beginning  of 
the  stroke  of  the  engine,  the  paper-drum  is  started 
from  rest  and  it  reaches  its  highest  speed  near  the 


THE  STEAM-ENGINE   INDICATOR.  49 

middle  of  the  stroke;  it  comes  to  rest  at  the  end  of 
the  stroke.  On  a  high-speed  engine  an  appreciable 
force  is  required  to  start  the  drum;  this  force  de- 
creases regularly  and  becomes  zero  when  the  drum 
attains  its  highest  speed;  a  regularly  increasing  force 
in  the  contrary  direction  is  required  to  stop  the  drum. 
If  we  consider  the  drum  at  the  beginning  of  a  stroke 
with  the  cord  wound  on  the  base  of  the  drum,  it  is 
evident  that  the  cord  must  exert  a  pull  equal  to  the 
sum  of  the  tension  of  the  spring  and  the  force  required 
to  start  the  drum;  and  the  stretch  of  the  cord  will 
be  proportioned  to  the  total  pull  it  exerts,  so  that 
the  cord  is  longer  at  the  beginning  of  the  stroke. 
As  the  drum  moves  toward  the  middle  of  the  stroke 
the  extra  force  decreases  and  becomes  zero,  so  that 
the  cord  attains  its  normal  length  under  the  tension 
of  the  spring  when  the  drum  attains  its  highest 
speed.  As  the  drum  slows  down  during  the  latter 
part  of  its  stroke  the  force  required  to  bring  it  to 
rest  is  subtracted  from  the  tension  of  the  spring,  and 
the  pull  on  the  cord  is  decreased  and  its  length  di- 
minishes. The  effect  of  this  action  is  to  lengthen  the 
diagram  at  both  ends.  During  the  return-stroke  the 
sequence  of  events  is  repeated  in  reversed  order.  At 
the  beginning  of  the  stroke  the  drum  is  started  by 
the  spring,  and  the  pull  on  the  cord  is  reduced;  at 
the  middle  of  the  stroke  the  cord  attains  its  normal 
length;  at  the  end  of  the  stroke  the  drum  is  brought 
to  rest  by  an  additional  pull  on  the  cord. 


$0  THE   STEAM-ENGINE  INDICATOR. 

The  action  just  described  is  well  illustrated  by  dia- 
grams taken  at  regular  intervals  from  an  engine  as 
it  starts  from  rest  and  comes  up  to  a  high  speed,  pro- 
vided, of  course,  that  a  long  cord  is  used.  At  first 
the  diagrams  are  notably  short  on  account  of  the 
varying  tension  of  the  drum  spring,  as  stated  in  the 
preceding  section.  As  the  speed  of  the  engine  in- 
creases the  inertia  of  the  paper-drum  lengthens  the 
diagram  till  it  attains  its  normal  length,  and  at  high 
speed  it  may  show  a  notable  excess  of  length. 

If  the  engine  had  a  slotted  crosshead  instead  of  a 
connecting-rod,  the  force  required  to  give  velocity 
to  the  drum  would  vary  uniformly  from  the  middle 
to  the  end  of  the  stroke,  and  the  cord  would  stretch 
and  contract  uniformly  so  that  the  only  effect  of  the 
inertia  of  the  drum  would  be  to  change  the  length 
of  the  diagram,  but  not  to  change  its  form.  A  dia- 
gram from  an  engine  with  a  connecting-rod  will  suf- 
fer distortion  from  the  effect  of  the  inertia  of  the 
paper-drum,  which  distortion  will  be  larger  as  the 
speed  increases,  and  will  increase  with  the  length  of 
the  cord.  The  conclusion  is  that  a  long  cord  is  to 
be  avoided  especially  for  a  high-speed  engine.  The 
effect  of  inertia  may  be  reduced  by  using  a  smaller 
and  a  lighter  drum,  as  is  sometimes  done  for  high- 
speed engines. 

Some  indicator-makers  purposely  use  a  short 
drum  spring  with  the  idea  that  its  increasing  ten- 
sion will  compensate  for  the  effect  of  inertia.  But 


THE   STEAM-ENGINE  INDICATOR.  51 

the  compensation  cannot  be  exact,  and  to  be  of  use 
would  require  adjustment  for  varying  speeds,  which 
would  be  troublesome,  if  not  practically  impossible. 

Friction    of    the    Paper-drum. — The    most    serious 
error  of  the  paper  drum  \\hen  a  long  cord  is  used  is 


FIG.  37. 

due  to  friction,  which  depends  en  the  condition  of 
the  bearing  surfaces.  Consequently  if  a  long  cord  is 
unavoidable  the  bearing  surfaces  should  be  carefully 
cleaned  and  oiled  to  avoid  friction. 


If  there  is  appreciable  friction  of  the  drum,  then, 
with  a  long  cord,  the  drum  will  pause  at  the  begin- 
ning of  a  stroke  till  the  tension  of  the  cord  is  in- 


52  THE   STEAM-ENGINE   INDICATOR. 

creased  enough  to  overcome  the  friction  and  start 
the  drum.  On  the  return-stroke  there  will  be  a 
similar  pause  till  the  pull  of  the  cord  is  reduced 
enough  to  allow  the  tension  of  the  spring  to  s  art  the 
drum.  The  effect  is  to  shorten  the  diagram  at  both 
ends  and  to  distort  the  diagram.  If  Fig.  37  repre- 
sents the  true  indicator  diagram  the  effect  of  friction 
and  a  long  cord  is  equivalent  to  leaving  gaps  at  aa 
and  bb'  and  closing  up  the  two  partial  diagrams  to 
give  an  apparently  complete  diagram  as  shown  by 
Fig.  38.  Like  other  errors  of  the  paper-drum,  this 
may  be  eliminated  by  using  a  short  cord. 

In  conclusion  attention  should  again  be  called  to 
the  fact  that  elasticity  (i.e.,  lack  of  rigidity)  of  the 
reducing  motion  or  of  its  support  will  have  the  fame 
effect  as  elasticity  of  cord,  and  that  wire  can  be  sub- 
stituted for  cord  only  when  it  can  be  kept  taut  so  that 
it  will  not  sway  back  and  forth. 

Errors  affecting  the  Pencil-motion. — The  errors  that 
affect  the  record  of  pressures  may  be  distinguished  as 

(1)  errors  of  geometric  design  of  the  pencil-motion; 

(2)  errors  due  to  friction  and  backlash;  (3)  errors  due 
to  pencil-friction;  (4)  errors  due  to  size  of  piston;  (5) 
errors  due  to  the  spring;  (6)  errors  due  to  inertia. 

A  discussion  of  these  several  errors  is  of  import- 
ance in  so  far  as  it  may  show  how  they  can  be  re- 
duced, but  it  is  not  possible  as  yet  to  determine  the 
gross  error  of  an  indicator  from  the  sum  of  the  in- 
dividual errors. 


THE   STEAM-ENGINE  INDICATOR.  53 

Design  of  Pencil-motion. — The  geometric  design  of 
a  pencil-motion  can  be  tested  by  drawing  a  diagram 
on  an  enlarged  scale,  with  extreme  positions  and  a 
proper  number  of  intermediate  positions.  The  de- 
sign will  usually  be  found  to  be  imperfect;  the  pencil 
does  not  draw  an  exactly  straight  line  and  the  mo- 
tion of  the  pencil  is  not  an  exact  copy  (on  an  en- 
larged scale)  of  the  motion  of  the  piston;  but  the 
imperfections  are  insignificant  compared  with  other 
unavoidable  errors. 

Backlash  and  Friction. — The  backlash  and  friction 
of  an  indicator  may  be  tested  as  follows:  first  press 
the  pencil  up  with  the  tip  of  the  finger,  release  it  and 
draw  an  atmospheric  line,  then  draw  another  atmos- 
pheric line  after  the  pencil  has  been  pressed  down. 
The  distance  between  the  atmospheric  lines  with  a 
good  indicator  is  liable  to  be  from  o.oi  to  0.02  of  an 
inch.  It  is,  however,  probable  that  the  influence  of 
friction  and  backlash  will  be  less  than  the  amount 
thus  determined  when  the  indicator  is  in  service,  as 
jar  and  vibration  are  likely  to  diminish  their  effect. 

Pencil- friction. — The  pressure  of  the  pencil  on  the 
paper  should  be  only  enough  to  give  a  clear  line  that 
can  be  seen  in  a  good  light.  The  influence  of  pencil- 
friction  is  to  make  the  pencil  lag  behind  its  true  po- 
sition. The  steam-line  is  likely  to  be  too  low  and  the 
back-pressure  line  too  high;  the  expansion-line  will 
not  be  as  steep  as  it  should  be,  and  the  compression- 
line  will  be  too  steep.  If  there  are  oscillations  in  the 


54  THE   STEAM-ENGINE   INDICATOR. 

diagram  due  to  inertia  they  may  change  some  of 
these  effects;  thus  the  steam-line  may  be  too  high 
if  the  pencil  falls  to  it  after  an  oscillation.  In  gen- 
eral the  tendency  of  pencil-friction  is  to  reduce  the 
area  of  the  diagram.  With  light  pressure  the  re- 
duction is  not  large;  pressure  enough  to  give  a  bold 
diagram  may  reduce  the  area  from  three  to  five  per 
cent.  A  heavy  pencil-pressure  will  entirely  spoil  the 
diagram. 

Error  due  to  Expansion  of  Piston. — The  piston  of 
an  indicator  is  made  with  an  area  of  one  square  inch 
when  it  is  cold  and  has  a  slightly  larger  area  on  ac- 
count of  expansion  when  hot.  The  error  from  this 
source  may  amount  to  one-half  of  one  per  cent. 

Error  of  the  Spring. — The  pressure  of  the  steam  in 
the  cylinder  of  the  engine  is  weighed  by  the  indi- 
cator spring;  all  other  parts  of  the  indicator  may  be 
considered  as  conveniences  for  recording  the  indica- 
tions of  the  spring.  A  spring,  when  used  for  weigh- 
ing or  measuring  force,  has  certain  inherent  defects, 
and  further,  when  used  in  an  indicator,  is  subjected 
to  unfavorable  conditions;  all  of  which  require  par- 
ticular attention. 

In  the  first  place  a  spring  is  slow.  For  example, 
if  a  ten-pound  weight  is  cautiously  applied  to  a  ^ood 
spring  balance,  the  balance  is  likely  to  show  a  trifle 
less  than  ten  pounds.  On  the  other  hand,  if  there 
are  two  weights  hung  on  the  balance,  a  ten-pound 
weight  and  a  five-pound  weight,  and  if  the  five- 


THE   STEAM-ENGINE  INDICATOR.  55 

pound  weight  is  cautiously  removed,  the  balance  is 
likely  to  show  a  trifle  more  than  ten  pounds.  In 
either  case  the  spring  is  said  to  be  slow,  that  is,  the 
true  record  is  not  shown  immediately.  The  slowness 
may  be  almost  entirely  overcome  by  jarring  the  bal- 
ance. The  spring  of  an  indicator  is  not  likely  to  show 
much  error  from  this  source  in  service,  as  the  piston 
is  in  almost  continuous  motion  and  there  are  likely  to 
be  vibrations  transmitted  to  it  from  the  engine;  but 
careful  tests  of  an  indicator  spring  out  of  the  indica- 
tor always  show  slowness,  which  must  not  be  mis- 
interpreted. 

In  the  second  place  a  spring  gives  only  coarse  in- 
dications. This  is  well  illustrated  by  comparing  a 
spring  balance  with  a  platform  balance  which  has 
knife-edges  in  good  condition.  But  a  spring  bal- 
ance weighing  up  to  20  pounds  will  weigh  to 
ounces,  which  corresponds  to  about  one-third  of  one 
per  cent.  Careful  investigations  of  indicator  springs 
out  of  the  indicator  and  at  ordinary  temperatures 
show  that  they  may  be  expected  to  have  an  ac- 
curacy of  one-fourth  of  one  per  cent.  It  may  be  con- 
sidered that  under  favorable  circumstances  a  spring 
is  good  enough  for  engineering  tests. 

Now  it  is  customary  to  consider  that  the  steam 
which  leaks  past  the  piston  of  an  indicator  falls  at 
once  to  the  pressure  of  the  atmosphere  and  to  212° 
F.,  and  further  to  assume  that  the  indicator  spring 
which  works  in  that  steam  has  the  same  tempera- 


$  THE  STEAM-ENGINE  INDICATOR. 

ture.  To  test  this  assumption  a  thermometer  was 
placed  inside  the  spring  of  an  indicator  and  the  tem- 
perature was  observed  while  the  indicator  was  in 
communication  with  the  cylinder  of  a  steam-engine. 
For  this  purpose  the  piston-rod  and  pencil-motion 
were  removed  and  the  thermometer  was  inserted 
through  the  hole  for  the  piston-rod.  The  thermome- 
ter showed  a  higher  temperature  than  212°  F.,  and 
the  temperature  further  increased  with  the  steam- 
pressure  in  the  cylinder;  a  series  of  experiments 
showed  that  the  temperature  indicated  by  the  ther- 
mometer corresponded  nearly,  though  not  exactly, 
to  the  average  steam-pressure  in  the  cylinder.  Tests 
on  another  indicator  with  a  loose  piston  which  gave 
excessive  leakage  showed  lower  temperatures  than 
were  found  for  an  indicator  which  had  its  piston  in 
normal  condition.  From  these  tests  it  appeared 
clearly  that  the  temperature  of  the  spring  is  main- 
tained at  a  high  degree  by  heat  transmitted  through 
the  piston  and  along  the  barrel  of  the  indicator,  and 
that  the  effect  of  steam  leaking  past  the  piston  is  to 
cool  the  spring,  rather  than  to  heat  it. 

The  investigations  of  the  temperatures  to  which  an 
indicator  spring  is  exposed  are  of  the  greatest  im- 
portance, because  it  is  well  known  that  springs  be- 
come weaker  at  high  temperatures.  Thus  a  certain 
indicator  spring  which  was  marked  80  pounds  to  the 
inch  gave  that  scale  at  100°  F.;  at  212°  F.  its  real 
scale  was  78  pounds  to  the  inch,  and  at  300°  F.  its 


THE  STEAM-ENGINE   INDICATOR.  57 

scale  was  hardly  75  pounds  to  the  inch.  A  certain 
6o-pound  scale  was  found  to  be  correct  at  212°  F., 
but  at  300°  F.  ils  scale  was  58  pounds  to  the  inch. 
Both  springs  gave  fairly  uniform  scales  for  a  given 
temperature,  whether  hot  or  cold. 

Indicator-makers  have  long  been  aware  of  the  in- 
fluence of  heat  on  the  scale  of  a  spring,  and  have  fur- 
nished springs  for  indicating  steam-engines,  and 
other  springs  for  air  or  water  pressure.  They  also 
test  springs  in  the  indicator  with  the  intent  that  they 
shall  have  the  proper  scale  when  in  use. 

The  proper  conclusion  from  the  experiments  on 
the  effect  of  temperature  on  the  scale  of  a  spring  is 
that  the  spring  should  be  outside  of  the  barrel  of  the 
indicator  and  so  exposed  to  the  air  that  its  tempera- 
ture would  not  be  much,  if  any,  greater  than  that  of 
the  atmosphere.  If  springs  were  so  placed  they 
could  be  rated  and  tested  cold,  and  the  most  trouble- 
some source  of  error  could  be  avoided. 

Indicator-testers. — Some  device  for  testing  indi- 
cators under  steam  is  employed  by  every  reliable  in- 
dicator-maker, and  such  devices  have  been  used  by 
steam-engine  experts  and  others.  Such  an  indicator- 
tester  usually  consists  of  a  receptacle  that  can  be 
filled  with  steam  at  varying  pressures,  to  which  in- 
dicators can  be  attached,  as  to  a  steam-engine;  there 
is  also  provision  for  measuring  the  pressure  of  the 
steam  by  a  mercury  column  or  by  a  pressure-gauge. 
For  convenience  in  testing  several  indicators  at  the 


58  THE   STEAM-ENGINE  INDICATOR. 

same  time  it  is  customary  to  provide  an  electrical  de- 
vice (much  like  that  shown  by  Fig.  26  in  general 
principle)  for  throwing  all  the  pencils  of  indica- 
tors undergoing  test  onto  their  cards  at  the  same  in- 
stant; there  is  also  a  device  for  drawing  out  the  pa- 
per-drums at  the  same  time.  Evidently  the  same 
end  could  be  attained  by  a  mechanical  device  such 
that  one  motion  of  the  hand  should  apply  the  pencils 
to  the  cards  and  draw  the  drum  cords;  by  having 
enough  observers  the  work  can  be  as  well  done  by 
hand.  There  is  no  difficulty  in  making  either  elec- 
trical or  mechanical  devices,  and  they  are  convenient 
if  not  essential  for  commercial  work;  but  they  do 
not  add  to  the  accuracy  or  reliability  of  the  fu  ida- 
mental  method  of  testing. 

In  using  such  a  tester  it  is  customary  to  raise  the 
steam-pressure  in  the  receptacle  by  stated,  amounts, 
five  or  tea  pounds  at  a  time,  and  then  set  in  motion 
the  device  for  drawing  the  drum  cards  and  applying 
the  pencils.  Thus  there  are  drawn  a  series  of 
straight  lines  on  the  cards,  which  are  drawn  to  rep- 
resent the  several  pressures  chosen.  An  atmos- 
pheric line  is  drawn  from  which  the  pressures  are 
afterwards  measured  with  the  proper  scale.  At  the 
instant  that  the  pencils  are  applied  to  the  cards  the 
pressure  of  steam  is  read  from  a  mercury  column  or 
a  pressure-gauge;  or  in  some  cases  the  mercury  col- 
umn is  made  to  close  the  electrical  circuit  and  work 
the  device  for  applying  the  pencils  and  moving  the 


THE    STEAM-ENGINE  INDICATOR.  59 

drums,  when  it  reaches  heights  that  give  the  desired 
pressures.  Here  again  the  added  complication  is  to 
be  considered  as  a  convenience,  and  care  must  be 
taken  that  it  does  not  introduce  an  additional  error. 

After  a  series  of  tests  has  been  made  with  rising 
pressures  it  is  customary  to  repeat  it  in  inverse  or- 
der with  falling  pressures,  before  removing  the  cards 
for  measurement.  Lines  drawn  at  the  same  pressures 
but  in  inverse  order  of  procedure  seldom,  if  ever, 
coincide;  the  lines  drawn  with  decreasing  pressures 
are  always  the  higher.  Two  atmospheric  lines  are 
drawn,  one  before  the  series  with  rising  pressure  and 
one  after  the  series  with  falling  pressure.  Finally 
the  cards  are  all  removed  and  measured. 

It  has  been  considered  that  the  discrepancy  be- 
tween tests  with  rising  and  with  falling  pressures  can 
be  attributed  to  friction  and  to  the  slowness  of  the 
spring  to  respond  to  a  change  of  pressure;  they  cer- 
tainly tend  to  produce  such  discrepancy.  But  the 
discrepancy  is  due  in  larger  degree  to  the  varying 
temperature  of  the  spring.  Tests  on  an  experimental 
indicator  which  has  its  spring  out  of  the  steam  con- 
firm this  view.  The  indicator  and  spring  are  heated 
rapidly  by  rising  steam-pressure,  but  lose  heat  slowly 
by  radiation  when  the  pressure  falls.  Tests  made  with 
rising  pressures  are  the  more  regular,  and  there  is 
reason  for  relying  on  them  alone. 

All  indicator-testers  of  the  sort  described  have  one 
radical  defect,  namely,  the  indicator  should  be  in  con- 


60  THE   STEAM-ENGINE   INDICATOR. 

tinual  motion  in  order  to  simulate  the  conditions  of 
service,  while  the  pressure-gauge  or  the  mercury  col- 
umn (more  especially  the  latter)  should  be  at  rest 
when  the  pressure  is  read.  These  conditions  are 
clearly  incompatible;  it  is  customary  to  change  pres- 
sures rather  slowly,  since  by  that  means  only  can  the 
gauge  or  mercury  column  be  made  to  work  prop- 
erly. It  has  been  thought  that  this  slow  change  of 
pressure  and  the  consequent  slow  motion  of  the  in- 
dicator piston  gives  rise  to  excessive  friction  at  the 
piston,  and  the  discrepancy  of  tests  with  rising  and 
with  falling  pressures  has  been  charged  to  this  ac- 
tion. It  is  not  possible  at  present  to  confirm  or  con- 
fute this  idea. 

An  indicator-tester  in  the  laboratory  of  the  Massa- 
chusetts Institute  of  Technology  is  designed  to  over- 
come the  difficulty  attributed  to  testers  already  de- 
scribed. In  the  first  place  the  indicators  are  attached 
to  a  cylinder  to  which  steam  is  supplied  and  from 
which  steam  is  exhausted  by  a  plain  slide-valve. 
There  is  no  piston  in  the  cylinder,  and  it  is  necessary 
to  drive  the  slide-valve  by  power.  Reservoirs  are 
provided  from  which  steam  is  supplied  to  the  valve- 
chest  and  to  which  the  exhaust  may  pass;  the  pres- 
sures in  these  reservoirs  can  be  controlled  so  that  the 
steam-pressures  and  exhaust-pressures  in  the  cylin- 
der may  be  made  to  vary  as  desired.  It  is  customary 
to  make  the  exhaust-pressure  five  or  ten  pounds  less 
than  the  steam-pressure,  and  to  vary  both  together 


THE  STEAM-ENGINE   INDICATOR.  6 1 

so  as  to  maintain  this  difference.  Diagrams  are 
taken  as  in  ordinary  service  at  any  desired  speed  of 
revolution,  and  it  is  seen  that  the  indicator  is  not 
affected  by  excessive  friction  as  charged  against 
other  testers.  Two  mercury  columns  are  employed, 
one  to  measure  the  steam-pressure  and  the  other  to 
measure  the  back-pressure.  Communication  be- 
tween the  first  mercury  column  and  the  cylinder  is 
open  only  when  the  slide-valve  is  wide  open,  and 
the  second  mercury  column  is  in  communication 
with  the  same  cylinder  when  the  slide-valve  is  closed 
to  the  steam  and  is  open  for  exhaust.  There  is  con- 
sequently no  difficulty  about  reading  the  mercury 
columns,  which  remain  steady  or  nearly  so.  The  pa- 
per-drum is  given  only  a  short  motion,  and  the  indi- 
cator draws  a  small  rectangular  diagram  with  hori- 
zontal lines  drawn  at  known  pressures.  The  error 
of  one  line  (for  example,  the  steam-line)  is  charge- 
able to  friction  and  to  error  of  scale;  but  the  mean 
error  of  both  lines  should  be  free  from  error  due  to 
friction  and  should  be  chargeable  to  error  of  scale 
only.  The  instrument  described  lacks  conveniences 
for  rapid  testing  and  could  not  be  used  commer- 
cially; even  for  laboratory  work  it  has  been  found 
troublesome  until  observers  have  acquired  facility 
after  much  practice.  It  is  believed  that  its  princi- 
ples are  correct  and  that  the  difficulties  in  using  it 
can  be  overcome.  The  conclusion  from  tests  that 
have  been  made  shows  that  springs  are  liable  to  an 


62  THE  STEAM-ENGINE   INDICATOR. 

error  of  5  per  cent  from  their  rated  scales;  if  a 
true  mean  scale  of  a  spring  is  determined  the  devia- 
tion from  that  scale  is  liable  to  be  2  per  cent. 
Springs  are  liable  to  be  weak,  that  is,  they  record 
too  high  pressures  and  give  too  large  powers  for  en- 
gines indicated. 

Effect  of  Piping. — It  is  advisable  especially  with 
high-speed  engines,  that  the  connection  from  the  in- 
dicator to  the  cylinder  shall  be  short  and  direct.  In 
some  cases  the  indicator  cock  may  be  screwed  directly 
into  the  wall  of  the  cylinder,  or  a  short  nipple  and 
coupling  may  suffice.  Commonly  an  elbow  is  re- 
quired to  bring  the  indicator  erect;  an  indicator  may, 
however,  be  used  with  the  paper-drum  horizontal 
when  convenient. 

Sometimes  the  indicator  is  connected  to  both  ends 
of  the  cylinder  of  a  steam-engine  so  that  diagrams 
may  be  taken  from  either  end  as  desired.  This  in- 
volves the  use  of  a  pipe  leading  to  each  end  of  the 
cylinder,  with  a  three-way  cock  (see  Fig.  20)  at  the 
middle;  the  steam  on  the  way  to  the  indicator  must 
make  two  turns,  one  at  the  elbow  near  the  end  of  the 
cylinder  and  one  at  the  three-way  cock,  and  it  must 
traverse  a  length  of  pipe  depending  on  the  size  of 
the  engine.  The  resistance  of  the  pipe  and  the  turns 
causes  the  changes  of  pressure  at  the  indicator  to 
lag  behind  the  changes  in  the  cylinder.  The  steam- 
line  will  be  too  low  and  the  back-pressure  line  too 


THE   STEAM-ENGINE  INDICATOR.  63 

high;  on  the  other  hand  the  cut-off  will  be  delayed 
and  the  expansion-line  will  be  too  high. 

In  addition  to  the  distortions  of  the  diagram  just 
noted,  it  is  liable  to  be  affected  by  rather  unaccount- 
able oscillations.  The  mean  effective  pressure  of  the 
distorted  diagram  may  be  either  more  or  less  than 
the  true  mean  effective  pressure.  In  the  first  place, 
lowering  the  steam-line  and  raising  the  back-pres- 
sure line  tends  to  reduce  the  mean  effective  pressure, 
while  delaying  the  cut-off  and  raising  the  expansion- 
line  tends  to  increase  it.  The  only  direct  conclu- 
sions from  the  somewhat  discordant  tests  on  the  ef- 
fect of  piping  on  the  mean  effective  pressure  are  that 
piping  should  be  avoided,  especially  on  high-speed 
engines,  and  that  when  such  piping  must  be  used  it 
should  not  be  less  than  three-quarter-inch  pipe,  and 
inch  pipe  is  somewhat  better.  Very  large  engines 
may  have  pipe  as  large  as  one  and  a  half  inches  in 
diameter.  All  such  piping  should  be  wrapped  to 
avoid  radiation,  especially  when  exposed  to  wind,  as 
on  a  locomotive.  Marine  engines  are  habitually  in- 
dicated in  this  manner,  so  that  the  results,  unless  for 
very  high-speed  engines,  are  likely  to  be  concordant. 

Piping  for  indicators  should  be  carefully  done, 
using  only  a  little  red-lead  in  making  joints,  and  ap- 
plying it  so  that  it  may  not  get  into  the  pipe  and 
thence  be  blown  into  the  indicator. 

Mean  Effective  Pressure. — The  diagram  from  an 
engine  without  cut-off  or  compression  and  with 


64 


THE   STEAM-ENGINE   INDICATOR. 


ample  ports  and  passages  is  a  rectangle.  The  width 
of  the  diagram  measured  with  the  proper  scale  gives 
at  once  the  effective  pressure  on  the  piston;  mean- 
ing by  the  effective  pressure,  the  difference  between 
the  steam-pressure  during  the  working-stroke  and 
the  back-pressure  during  the  exhaust-stroke.  Now 
the  pressure  of  the  steam  for  a  diagram  like  Fig.  36 
varies  from  point  to  point,  and  the  mean  effective 
pressure  may  be  determined  from  the  mean  width  of 
the  diagram. 

To  determine  the  mean  effective  pressure  it  is  con- 
venient to  divide  the  length  of  the  diagram  into  ten 
equal  parts,  as  shown  by  light  lines  in  Fig.  39.  The 
width  of  these  several  parts  can  be  measured  with 
the  proper  scale  on  lines  drawn  at  the  middle  of 
them,  as  shown  by  heavy  lines  in  Fig.  39.  In  pre- 


\ 


FIG.  39. 

paring  a  diagram  for  measuring  the  mean  effective 
pressure  a  scale  of  convenient  length  may  be  laid 
across  it  diagonally  so  that  zero  shall  come  on  a  ver- 
tical line  at  one  end  of  the  diagram,  and  100  on  the 
line  at  the  other  end,  as  shown  by  Fig.  39.  Then 


THE   STEAM-ENGINE   INDICATOR. 


draw  lines  as  shown  at  5,  15,  25,  etc.,  and  on  them 
measure  the  width  of  the  diagram  at  ten  points,  using 


FIG.  40. 

the  proper  scale.  The  mean  effective  pressure  may 
be  calculated  by  taking  one-tenth  of  the  sum  of  the 
ten  several  widths,  as  follows: 

ist  width 42 


2d 
3d 
4th 
5th 
6th 
7th 
8th 
9th 
loth 


54 
58 
51 
40 
31 
25 

21 

14 

4 


Sum 340.5 

y1^  of  sum,  m.  e.  p 34  pounds 

If  desired  more  or  less  than  ten  widths  can  be 
taken;  for  example,  twelve  widths  can  be  measured 
and  then  the  mean  effective  pressure  will  be  V12  of 
the  sum  of  the  twelve  several  widths. 

When  a  diagram  is  taken  from  an  engine  with  a 


66 


THE   STEAM-ENGINE   INDICATOR. 


short  cut-off,  the  expansion-line  may  run  below  the 
back-pressure  line,  forming  a  loop,  as  shown  by  Fig. 
41.  On  this  diagram  the  steam-pressure  is  greater 


FIG.  41. 

than  the  back-pressure  on  the  first  five  lines  drawn 
across  it.  On  the  lines  numbered  from  6  to  10  the 
back-pressure  is  the  greater.  Roughly,  the  steam 
does  work  on  the  piston  for  the  first  half  of  the  dia- 
gram, while  for  the  second  half  the  piston  does  work 
to  force  the  steam  out  against  the  pressure  of  the 
atmosphere.  The  mean  effective  pressure  will  be 
calculated  by  adding  the  first  five  widths  and  by  sub- 
tracting the  last  five  widths,  and  then  dividing  by  ten 
as  before;  thus: 

ist  width 43.0 


3d 
4th 
5th 

6th 
7th 
8th 
gth 
loth 

Di 
J*  diffe 

•            II-5 

4.8 

*     13 

«     i.o 

.    18  2 

'       2.8 

'                                               J.  O 

-     Sum.  .  .  . 

.    72  4. 

THE   STEAM-ENGINE  INDICATOR. 


The  preceding  explanation,  while  it  leads  properly 
to  the  correct  method  of  calculating  mean  effective 
pressure  for  a  diagram  with  a  loop,  is  not  strictly 
logical,  for  in  reality  work  is  done  by  the  steam  on 
the  piston  throughout  the  working-stroke,  and  the 
piston  does  work  on  the  steam  to  force  it  out  of  the 
cylinder  against  the  pressure  of  the  atmosphere, 
throughout  the  exhaust-stroke,  Fig,  41  may  be 


M 


To  N 


FIG.  42. 

separated   into    two    parts,    as    shown    by    Figs.    42 
and  43. 

In  Fig.  42  the  line  CD  represents  the  admission 
and  expansion  of  steam  during  the  working-stroke  of 
the  piston.  The  line  MN,  drawn  at  14.7  pounds  be- 
low the  atmospheric  line,  is  called  the  line  of  zero 
pressure,  or  the  absolute  vacuum  line.  Pressures 
measured  from  this  line  give  the  real  pressure  of 
steam;  thus  at  the  first  line  the  pressure  is  64 
pounds,  that  is,  49.3  pounds  above  the  atmosphere 
(measured  from  the  atmospheric  line),  plus  14.7 
pounds,  equal  to  64  pounds.  Since  the  steam  in  the 
cylinder  of  the  engine  is  shut  off  from  the  atmos- 


68  THE   STEAM-ENGINE  INDICATOR. 

phere,  its  total  pressure  does  not  depend  on  the  at- 
mosphere; it  must,  however,  be  calculated  from  the 
pressure  of  the  atmosphere  as  shown  by  a  barometer, 
for  both  indicators  and  steam-gauges  show  the  pres- 
sure above  the  pressure  of  the  atmosphere. 

In  much  the  same  way  Fig.  43  shows  the  exhaust 
and  compression,  referred  both  to  the  atmospheric 
line  AB  and  the  line  MN  of  zero  pressure. 

The  work  done  by  the  steam  on  the  piston  can  be 
calculated  from  the  mean  effective  pressure  of  Fig. 
42,  and  the  work  done  by  the  piston  during  exhaust 
may  be  calculated  from  Fig.  43,  as  represented  be- 
low: 

Fig.  42.                                 Fig.  43.  Difference. 

ist  line 64.0                                 21. o  43.0 

17-0  30.0 

16.8  11.5 

16.5  4.8 

16.4  1.3 

90.6 

16.2  —  i.o 

16.1  —  2.8 

16.0  —  4.0 

15-9  -  5-o 

15-7  -  5-4 

-18.2 

10)167.6       Difference...    10)72.4 


3d 

.  ..   47.0 

id     " 

28  i 

ju 
4.th    " 

.    .    .        ^,U.  3 

.    21.1 

5th   "    .... 

.  ...     17.7 

6th    "    .... 

...     15-2 

7th    " 

.     Ill 

8th    " 

9th    " 

.  .  .    10  9 

Sum  

10)240.0     Sum.  .  . 

m.  e.  p.  .  . 

24.0     m.  e.  p, 

16.76     m.  e.  p 7.24 

Resultant  m.  e.  p.  24.0  —  16.76  =  7.24  pounds. 

The  column  headed  Fig.  42  gives  the  several 
widths  for  the  corresponding  diagram,  and  the  col- 
umn headed  Fig.  43  does  the  same  for  its  diagram. 
The  resultant  m.  e.  p.  obtained  by  subtracting  the 


THE   STEAM-ENGINE  INDICATOR.  09 

m.  e.  p.  for  the  second  column  from  the  m.  e.  p.  for 
the  first  column  is  the  same  as  that  already  found 
from  Fig.  41.  Under  the  heading  of  Differences  are 
given  the  results  obtained  by  subtracting  the  num- 
bers of  the  second  column  from  those  in  the  first  col- 
umn. These  differences  are  clearly  the  widths  of 
Fig.  41  at  the  corresponding  lines;  the  differences 

C 


b-, 

[ 

[ 

1 

6 

T" 

FIG.  43- 

are  negative  for  the  6th,  7th,  8th,  9th,  and  loth  lines 
corresponding  to  the  widths  of  the  loop  for  Fig.  41. 
The  calculation  at  the  right  hand  is  evidently  a 
transcript  of  the  calculation  for  Fig.  41,  and  would 
give  a  correct  result  whether  or  not  there  is  a  loop, 
for  without  a  loop  there  would  be  no  negative  differ- 
ences. Finally  it  is  evident  that  the  subtraction  of 
widths  of  the  loop  in  the  calculation  for  Fig.  41  is 
a  purely  arithmetical  operation,  due  to  the  fact  that 
the  back-pressure  happens  to  be  higher  than  the  end 
of  the  expansion-line. 

It  is  evident  that  the  mean  width  of  an  indicator 
diagram  can  be  obtained,  when  the  area  in  square 


70  THE   STEAM-ENGINE  INDICATOR. 

inches  is  known,  by  dividing  its  area  by  the  length  in 
inches.  The  area  can  be  conveniently  measured  by 
aid  of  a  planimeter,  which  will  now  be  described. 

Amsler  Planimeter. — It  is  customary  to  determine 
the  mean  effective  pressure  of  indicator  diagrams 
from  the  area  of  the  diagram  measured  by  aid  of 
a  planimeter  like  that  represented  by  Fig.  44.  This 
instrument  has  two  arms,  the  tracing-arm  HF  and 
the  guiding-arm  HP,  hinged  together  at  H.  The 


FIG.  44. 

guiding-arm  has  a  needle-point  at  P  which  serves 
as  a  pivot  to  locate  the  instrument,  and  at  -F  is  a 
tracing-point.  At  D  on  the  tracing-arm  is  a  meas- 
uring and  recording  wheel. 

The  planimeter  is  used  on  a  drawing-board  or 
table  covered  with  paper  or  cardboard  so  as  to  give 
a  flat,  smooth,  unglazed  surface  for  the  wheel  to  roll 
on.  The  indicator  diagram  is  pinned  down  on  the 
table  and  the  planimeter  is  set  as  in  Fig.  45,  so  that 
the  tracing-point  may  be  carried  around  the  outline 
of  the  diagram  without  cramping  the  instrument  and 
without  drawing  the  measuring-wheel  over  the  edge 
of  the  card  or  paper  on  which  the  diagram  is  drawn. 


THE   STEAM-ENGINE   INDICATOR.  ? 'I 

The  measuring-wheel  is  divided  into  ten  parts  and 
subdivided  into  hundredths.  A  fixed  vernier  carries 
an  index  and  a  special  scale  for  finer  readings;  the 
use  of  the  vernier  will  be  described  later,  it  being 


FIG.  45. 

sufficient  for  the  present  to  take  account  of  the  fixed 
index  only. 

To  measure  the  area  of  a  diagram,  locate  a  con- 
venient point,  as  F,  by  a  light  prick  with  the  point  of 
a  needle.  Place  the  tracing-point  F  of  the  planim- 
eter  at  this  point,  and  set  the  wheel  by  hand  to  read 
zero  at  the  fixed  index.  Move  the  tracing-point 
over  the  outline  of  the  diagram  toward  the  right, 
and  stop  at  the  point  which  was  located  by  the 


72  THE   STEAM-ENGINE   INDICATOR. 

needle-prick.  Read  the  scale  of  the  wheel  at  the 
fixed  index;  the  main  divisions  represent  square 
inches,  and  the  subdivisions  represent  tenths. 

It  is  very  important  that  the  planimeter  shall  start 
and  stop  at  the  same  point;  a  slight  deviation  makes 
a  large  difference  in  the  reading  of  the  scale  on  the 
wheel.  It  is  for  this  reason  that  the  starting-point  is 
located  with  a  needle;  sometimes  it  may  be  prefer- 
able to  mark  the  starting-point  by  a  pencil-line,  in 
which  case  greater  care  is  required  in  starting  and 
stopping.  It  is  also  important  that  the  diagram 
shall  be  traced  exactly;  some  practice  is  required  to 
gain  skill  and  rapidity  in  the  use  of  the  planimeter, 
which  is  an  exact  and  delicate  instrument. 

Fig.  46  represents  a  scale  with  divisions  and  sub- 
divisions into  tenths,  that  can  be  moved  past  a  fixed 


LJ 

it  1  I  1   I   1  1°  1 

o1  '  '  ' 

1   1   1    1   1    1   t    1   1 

1   1    1    1       Mill 
1                  2 

FIG.  46. 

index,  which  in  the  figure  is  something  beyond  the 
division  1.2  of  the  scale.  The  scale  of  the  vernier  has 
ten  divisions,  but  they  are  shorter  than  the  subdi- 
visions of  the  main  scale;  the  ten  divisions  of  the 
vernier  occupy  the  same  space  as  nine  divisions  of 
the  main  scale,  and  consequently  each  division  of  the 
vernier  is  one-tenth  of  a  subdivision  of  the  scale 
shorter  than  one  of  the  subdivisions  of  the  scale.  It 


THE   STEAM-ENGINE   INDICATOR.  ?$ 

will  be  noted  that  the  6th  division  of  the  vernier  co- 
incides with  a  subdivision  of  the  scale;  the  5th  di- 
vision is  consequently  1/10  of  a  subdivision  of  the 
scale  from  the  adjacent  division  of  the  scale,  that  is 
to  say,  it  is  1/i0o  of  a  whole  division  of  the  scale  from 
that  mark;  the  4th  vernier  division  is  2/10o  ahead  of 
the  adjacent  mark;  the  3d  division  is  3/100;  the  2d 
division  is  ViooJ  the  Ist  division  is  ViooJ  and  the  in- 
dex is  Vioo  ahead  of  the  mark  on  the  main  scale. 
The  index  consequently  reads  1.26  of  the  scale. 
Therefore  we  read  forward  on  the  scale  to  the  mark 
before  the  index,  and  then  forward  on  the  vernier  to 
that  division  of  the  vernier  which  coincides  with  a 
mark  on  the  scale. 

The  planimeter  represented  by  Fig.  44  measures 
areas  in  inches  and  decimals;  the  large  divisions 
give  the  number  of  square  inches,  the  subdivisions 
give  tenths,  and  hundredths  are  read  on  the  ver- 
nier. This  planimeter  has  a  tracing-arm  which  is 
four  inches  long  measured  from  the  hinje  to  the 
tracing-point,  and  the  circumference  of  the  wheel  is 
two  and  a  half  inches;  the  diameter  of  the  wheel  is 
0.7957  of  an  inch.  Some  planimeters  have  the  same 
size  wheel  and  have  an  arm  eight  inches  long;  if 
read  as  directed  for  Fig.  44,  the  readings  are  to  be 
multiplied  by  2  to  give  the  area  of  a  figure  in  square 
inches. 

Fig.   47  shows   a  planimeter   with   an   adjustable 
tracing-arm;  when  set  at  the  proper  length  (4  inches) 


74  THE   STEAM-ENGINE   INDICATOR. 

this  instrument  gives  areas  in  square  inches;  it  can 
also  be  set  to  read  in  square  feet  and  in  square  deci- 
meters. When  set  to  read  in  square  feet  one  entire 
revolution  of  the  wheel  corresponds  to  one-tenth  of  a 
square  foot,  and  the  divisions,  subdivisions,  and  the 


FIG.  47- 

vernier  give  hundredths,  thousandths,  and  ten-thou- 
sandths of  a  square  foot;  when  set  for  square  decime- 
ters one  revolution  of  the  wheel  corresponds,  to  a 
square  decimeter.  If  the  tracing-arm  is  made  eight 
inches  long,  one  revolution  of  the  wheel  corresponds 
to  20  square  inches. 

The  back  of  the  tracing-arm  carries  two  points, 
one  on  the  arm  near  the  tracing-point  and  one  on 
the  slide  near  the  hinge.  If  the  instrument  is  set  as 
represented  by  Fig.  48  so  that  the  distance  between 
these  points  is  equal  to  the  length  of  the  indicator 
diagram,  the  instrument  will  give  the  mean  height 
of  the  diagram  in  fortieths  of  an  inch;  if  the  diagram 
is  drawn  with  a  40  scale  the  instrument  gives  the 
mean  effective  pressure  immediately.  In  this  case 
one  revolution  of  the  wheel  corresponds  to  one 
hundred,  the  main  divisions  of  the  scale  give  the  tens, 


THE   STEAM-ENGINE   INDICATOR. 


75 


and  the  subdivisions  give  the  units,  while  tenths  are 
read  on  the  vernier.  If  the  diagram  is  drawn  with 
some  other  scale,  then  the  reading  of  the  instrument 


is  to  be  multiplied  by  the  scale  of  the  spring  and  di- 
vided by  40;  or  an  equivalent  operation  is  to  be  per- 


76 


THE  STEAM-ENGINE  INDICATOR. 


formed.  Thus  for  an  80  scale  the  readings  are  to  be 
doubled;  for  a  50  scale  the  readings  are  to  be  in- 
creased by  one-fourth;  while  for  a  30  scale  they  are  to 
be  diminished  by  one-fourth. 

To  get  a  conception  of  the  way  in  which  a  planim- 
eter  measures  an  area  we  may  proceed  as  follows. 
In  Fig.  49  let  hp  represent  the  tracing-arm  of  a 


FIG.  49. 

planimeter  measuring  4  inches  from  the  hinge  at  h  to 
the  tracing-point  />.   On  this  arm  there  is  a  wheel  at  w 


which  has  the  circumference  of  2^  inches;  its  diam- 
eter is  .7957  of  an  inch.  If  the  arm  hp  is  moved  di- 
rectly down,  parallel  to  itself,  the  wheel  will  measure 
the  distance  hi  that  the  arm  is  moved,  and  if  hi  is 


THE   STEAM-ENGINE  INDICATOR. 


77 


made  equal  to  2|  inches  the  wheel  will  make  one 
complete  revolution.  The  area  of  the  figure  hpqi  is 
4  X  2^  =  10  square  inches,  and  consequently  if  the 
wheel  w  has  its  scale  divided  into  ten  main  divi- 
sions each  one  will  correspond  to  one  square  inch  of 
area.  If  the  arm  hp  is  kept  parallel  to  itself,  as  shown 


in  Fig.  50,  but  moved  so  that  h  passes  along  the  in- 
clined line  ///,  the  wheel  will  roll  and  slide  as  it  passes 
from  iv  to  ,r;  it  will  roll  the  distance  yx  and  will  slide 
the  distance  wy.  The  sliding  does  not  affect  the  read- 
ing of  the  wheel,  but  the  distance  rolled  is  as  before 
the  height  of  the  figure  hpqi,  and  its  area  is  again 
4  X  2^  =  10  inches  after  the  wheel  has  rolled  one 
complete  revolution.  But  the  same  result  will  be  .ob- 
tained if  the  point  h  moves  on  a  curved  line  hi  in 
Fig.  51,  for  the  area  is  again  4  X  2^  =  10  inches  for 
one  revolution  of  the  wheel.  It  is  evident  that  the 
wheel  can  be  placed  anywhere  on  the  arm  hp,  or  it 
may  be  on  an  extension  of  the  arm,  as  in  Fig.  52. 

In  the  planimeters  shown  by  Figs.  44  to  48  the 
hinge  is  guided  by  the  guiding-arm  along  the  arc  of 


78  THE   STEAM-ENGINE  INDICATOR. 

a  circle,  but  that  is  only  a  matter  of  convenience,  and 
the  hinge  may  be  guided  along  a  straight  line,  as 


FIG.  52. 

shown  by  Fig.  55,  which  represents  a  special  form  of 
planimeter. 

In  Fig.  53  let  ab  be  an  arc  of  a  circle  on  which  the 
hinge  of  a  planimeter  is  guided  by  the  guiding-arm 


FIG.  53. 

hg.  If  the  wheel  is  set  with  its  index  at  zero  and  the 
tracing-point  is  carried  around  the  figure  pqrs,  the 
final  reading  of  the  wheel  will  give  the  area  of  the 
figure.  To  see  that  this  is  true,  consider  that  qi  is 
drawn  parallel  to  hp  and  that  the  wheel  will  record 
the  area  of  hpqi  while  the  tracing-point  moves  from 
p  to  q;  while  the  tracing-point  moves  from  q  to  r 


THE   STEAM-ENGINE   INDICATOR. 


79 


the  wheel  rolls  over  the  path  xy,  but  this  action  will 
be  compensated  by  a  reverse  operation  later;  again 
hs  is  parallel  to  ri  so  that  the  wheel  will  record  the 
area  of  the  figure  rshi  while  the  tracing-point  moves 
from  r  to  s',  the  figure  pqrs  is  completed  by  moving 
the  tracing-point  from  s  to  />,  during  which  the  wheel 
rolls  the  distance  zw,  which  is  equal  to  xy,  and  is 
rolled  in  the  contrary  direction  so  that  it  just  com- 
pensates the  first  action.  Now  we  can  get  the  area 
of  pqrs  by  adding  the  areas  of  hpqi  and  iqr  and  sub- 
tracting the  areas  of  rshi  and  hps\,  but  iqr  and  hps 
are  equal,  consequently  the  area  of  pqrs  is  equal  to 
hpqi  minus  hsri',  now  the  arm  hp  moves  down  in  pass- 
ing from  p  to  q  and  up  in  passing  from  rs,  so  that  the 
wheel  adds  the  area  of  hpqi  and  subtracts  the  area  of 
hsrif  and  consequently  the  final  reading  of  the  wheel 
gives  the  area  of  the  figure  pqrs. 

Coming  now  to  an  irregular  figure,  like  an  indi- 
cator diagram,  a  first  approximation  to  the*  area  can 


FIG.  54- 


be  had  by  replacing  the  actual  diagram  by  one  hav- 
ing   the    contour    abfklh.      The    individual    figures 


8O  THE   STEAM-ENGINE   INDICATOR. 

abed,  efgh,  and  iklm  can  be  measured  and  their 
areas  summed  up,  or  the  tracing-point  of  the  pla- 
nimeter  can  be  carried  entirely  round  the  figure, 
omitting  the  lines  dc  and  ig,  which  are  common  to 
two  individual  figures,  and  which  are  traced  in  oppo- 
site directions  when  the  figures  are  traced  separately. 
The  narrower  and  more  numerous  the  individual 
figures  the  closer  will  be  the  approximation;  conse- 
quently to  get  the  true  area  of  the  indicator  diagram 
it  is  sufficient  to  trace  its  outline  as  already  explained 
in  the  description  of  the  instrument. 

The  planimeter  represented  by  Fig.  44  has  an  arm 
which  is  4  inches  "long,  and  the  circumference  of  its 
wheel  is  2\  inches;  consequently  one  revolution  of  the 
wheel  corresponds  to  an  area  of  10  square  inches.  The 
scale  of  the  wheel  is  divided  into  ten  main  divisions, 
each  of  which  corresponds  to  one  square  inch  of 
area.  The  subdivisions  of  the  wheel  and  the  vernier 
allow  us  to  read  to  hundredths  of  a  square  inch. 

The  planimeter  shown  by  Fig.  47  can  be  set  so 
that  its  arm  is  4  inches  long,  and  as  its  wheel  has 
a  circumference  of  2^  inches,  the  main  divisions  of  its 
wheel  correspond  to  square  inches  of  area.  Another 
way  of  considering  this  matter  is  to  read  the  whole 
number  of  turns  of  the  wheel  from  a  counter  which 
will  be  seen  on  the  axis  of  the  wheel,  and  three  deci- 
mal figures  on  the  scale  and  vernier,  and  then  multi- 
ply by  10  to  get  the  area  in  square  inches.  The 
mark  to  which  the  tracing-arm  is  to  be  set  is  lettered 


THE   STEAM-ENGINE   INDICATOR.  8 1 

10  sq.  in.  A  planimeter  with  an  arm  8  inches  long 
and  a  wheel  2-|  inches  in  circumference  must  have 
the  number  of  turns  of  the  wheel  (and  decimals  of  a 
turn)  multiplied  by  20  to  give  square  inches. 

Area  and  Mean  Effective  Pressure. — To  get  the 
mean  effective  pressure  for  an  indicator  diagram,  we 
may  (i)  measure  the  area  in  square  inches  with  a 
planimeter,  (2)  divide  the  area  by  the  length  of  the 
diagram  in  inches  to  get  the  mean  height,  and  (3) 
multiply  the  mean  height  by  the  scale  of  the  spring. 
It  is  customary  and  convenient  to  change  the  order 
of  operations,  so  that  the  area  is  multiplied  by  the 
scale  of  the  spring,  and  the  product  is  divided  by  the 
length.  Thus  the  diagram  Fig.  39  has  an  area  of  1.13 
square  inches;  its  length  is  2  inches,  and,  with  a  scale 
of  60  pounds  to  the  inch,  its  mean  effective  pressure 
is 

Area  X  scale       1.13  X  60 

length  —     '  =  33-9  »•  e.  p. 

If  a  diagram  has  a  loop,  as  shown  by  Fig.  41,  page 
66,  the  main  portion  of  the  diagram  is  traced  by  the 
planimeter  moving  toward  the  right,  but  the  loop 
is  traced  moving  toward  the  left.  The  planimeter 
adds  the  main  portion  and  subtracts  the  loop,  which 
is  equivalent  to  subtracting  widths  of  the  loop  as  in 
the  calculation  on  page  68. 

The  planimeter  shown  by  Figs.  47  and  48  has  two 
points  on  the  back  of  the  tracing-arm,  and  the  dis- 


82  THE   STEAM-ENGINE   INDICATOR. 

tance  between  them  is  equal  to  the  length  of  the  arm 
from  hinge  to  tracing-point.  As  shown  by  Fig.  48, 
these  points  may  be  adjusted  to  the  length  of  the  in- 
dicator diagram,  and  then  the  reading  of  the  wheel 
gives  the  width  of  the  diagram  in  fortieths  of  an  inch, 
each  subdivision  of  the  scale  of  the  wheel  (hun- 
dredths  of  the  circumference)  being  read  as  one-for- 
tieth. If  the  scale  of  the  diagrams  is  40  pounds  to 
the  inch,  the  reading  of  the  wheel  gives  the  mean 
effective  pressure  directly.  To  understand  the  prin- 
ciple of  this  way  of  using  the  planimeter,  let  us  bear 
in  mind  that  the  area  corresponding  to  one  turn  of 
the  wheel  of  a  planimeter  is  equal  to  the  length  of  the 
arm  multiplied  by  the  circumference  of  the  wheel. 
To  get  the  mean  height  of  a  diagram  we  divide  the 
area  by  the  length  of  the  diagram.  If  then  the  length 
of  the  arm  is  made  equal  to  the  length  of  the  diagram, 
the  height  of  a  diagram  which  gives  one  turn  of  the 
wheel  will  be  just  equal  to  the  circumference  of  the 
wheel  (2.5  inches).  Since  the  wheel  is  divided  to 
hundredths  of  a  turn,  each  hundredth  will  correspond 
to  2'5/ioo  —  1/4o  °f  an  mcn-  Thus  we  see  why  this 
instrument  gives' mean  effective  pressure  directly  for 
a  40  scale.  For  any  other  scale,  multiply  by  the  scale 
and  divide  by  40. 

Coffin  Averaging  Instrument. — This  is  a  planimeter 
which  has  one  end  of  the  tracing-arm  guided  in  a 
straight  groove,  as  shown  by  Fig.  55.  It  can  be  used 
to  measure  areas  just  as  the  instrument  represented 


THE   STEAM-ENGINE   INDICATOR.  83 

by  Fig.  44  is  used.    Its  tracing-wheel  is  2.5  inches  in 
circumference,  and  its  arm  is  six  inches  long,  so  that 


FIG.  55. 

one  turn  of  the  wheel  corresponds  to  15  square 
inches.  The  scale  of  the  wheel  has  15  main  divisions, 
each  of  which  corresponds  to  one  square  inch  of 


84  THE   STEAM-ENGINE    INDICATOR. 

area;  each  main  division  is  subdivided  into  fifths,  so 
that  the  subdivisions  correspond  to  two-tenths  of  an 
inch;  finally  the  vernier  has  ten  divisions,  and  enables 
us  to  read  to  two  one-hundredths  of  an  inch.  This 
division  is  not  so  convenient  as  that  for  planimeters 
described  earlier,  but  the  instrument  is  intended  to 
be  used  in  another  way  to  be  explained. 

The  usual  way  of  determining  mean  effective  pres- 
sure is  as  follows:  The  diagram  to  be  measured  is 
placed  under  the  fixed  clips  at  the  left  so  that  one  end 
comes  to  the  vertical  edge,  and  the  atmospheric  line 
(or  a  convenient  line  parallel  to  it)  comes  to  the  hori- 
zontal edge  as  shown.  The  movable  clip  is  brought 
to  the  other  end  of  the  diagram.  The  tracing-point 
D  is  placed  at  the  end  of  the  diagram  near  the  mova- 
ble clip,  and  the  groove  in  which  the  "  hinge,"  or 
guided  point,  moves,  if  prolonged,  would  coincide 
with  the  other  end  of  the  diagram.  The  wheel  is  set 
at  zero,  and  the  diagram  is  traced  as  usual,  stopping 
at  D]  the  point  D  is  now  slid  along  the  movable  clip 
till  the  wheel  turns  back  to  zero;  the  distance  that  the 
tracing-point  is  moved  in  this  last  operation  is  equal 
to  the  mean  height  of  the  diagram,  and  can  be  meas- 
ured with  the  proper  scale.  When  the  contour  is  traced 
the  wheel  records  the  area  of  the  diagram,  and  this 
area,  divided  by  the  length  of  the  diagram,  gives  the 
mean  height  Dd,  Fig.  56.  When  the  tracing-point  is 
raised  from  D  to  d  the  area  of  the  figure  cdDe  is 
subtracted,  and  this  area  is  equal  to  that  of  the  figure 


THE   STEAM-ENGINE  INDICATOR. 


abDb;  consequently  the  tracing-point  will   come  to 
d  when  the  reading  of  the  wheel  is  reduced  to  zero. 


FIG.  56. 

The  height  of  the  diagram  measured  with  the  proper 
scale  gives  the  mean  effective  pressure. 


FIG.  57- 

Lippincott  and  Willis  Planimeters. — The  Lippincott 
planimeter  as  shown  by  Fig.  57  has  a  tracing-arm 


86  THE   STEAM-ENGINE   INDICATOR. 

HP,  and  a  guiding-arm  RH,  hinged  at  H,  and  so  far 
resembles  the  Amsler  planimeter;  but  it  has  a  wheel 
W  on  an  arm  CD  which  is  at  right  angles  with  the 
tracing-arm;  the  wheel  W  is  free  to  slide  on  the  arm 


FIG.  58. 

CD,  but  has  a  sharp  edge  so  that  it  cannot  slide  on 
the  paper;  the  arm  CD  is  a  glass  tube  closed  at  the 
ends,  as  shown  more  clearly  by  Fig.  58,  and  has  a 
paper  scale  inside  on  which  the  area  of  the  diagram 
or  the  mean  effective  pressure  can  be  read. 

Fig.  59  shows  a  modification  of  this  type  of  planim- 
eter, known  as  the  Willis  planimeter,  in  which  the 
glass  tube  is  replaced  by  a  steel  spindle  that  slides 
under  the  rollers  R  and  S  and  carries  the  wheel  W, 
which  traverses  over  an  enameled  scale.  The  prin- 
ciple is  of  course  just  the  same;  the  simpler  arrange- 
ment will  be  chosen  for  discussion. 

To  understand  the  action  of  this  instrument,  we 
may,  as  for  the  Ams'er  planimeter,  consider  the  effect 
of  moving  the  tracing-arm  parallel  to  itself  from  a 
position  hp,  Fig.  60,  to  a  position  iq\  clearly  the  only 
effect  on  the  wheel  is  to  make  it  slide  on  the  arm  cd 
a  distance  equal  to  hi,  the  height  of  the  rectangle 
hpqi't  perhaps  in  this  case  it  may  seem  better  to  say 


THE  STEAM-ENGINE  INDICATOR.  8/ 

that  the  arm  cd  is  drawn  through  the  wheel,  which 
remains  a  rest,  neither  rolling  nor  sliding  on  the 
paper.  If  the  arm  hp  is  4  inches  long,  and  the  area 


of  the  rectangle  hpqi  is  10  square  inches,  then  the 
wheel  slides  2.\  inches  on  the  arm;  in  this 
case  the  scale  on  the  arm  cd  is  made  2|  inches 
long,  and  is  divided  into  ten  parts  each  of  which 


88 


THE   STEAM-ENGINE   INDICATOR. 


corresponds  to  one  square  inch  of  area;  the  scale  is 
subdivided   for   tenths   of  a   square   inch,    and   hun- 


FIG.  60. 

dredths,  if  read,  must  be  estimated,  as  the  instrument 
has  no  vernier.     In  Fig.  61  the  wheel  rolls  from  w  to 


w      w     d 


w' 


FIG.  61. 

w" ,  while  the  arm  hp  moves  to  iq,  but  this  rolling 
does  not  affect  the  reading,  which  is  equal  to  w'w", 


THE   STEAM-ENGINE  INDICATOR. 


89 


that  is,  the  wheel  slides  on  the  arm  cd  a  distance  equal 
to  the  height  of  the  figure  hpqi,  and  with  a  proper 
scale  can  be  made  to  measuie  that  area  in  square 
inches. 

If  the  arm  hp  is  pivoted  about  a  point  as  in  Fig.  62, 
the  arm  cd  at  any  instant  will  have  two  motions:  (i) 
it  will  be  drawn  endwise  through  the  wheel,  and  (2) 


FIG.  62. 

it  will  swing  around  just  as  fast  as  the  arm  hp  does; 
the  first  action  affects  the  reading  on  the  scale,  and 
the  second,  which  makes  the  wheel  roll,  does  not.  A 
little  consideration  will  make  it  appear  that  the  arm 
cd  is  drawn  endwise  a  distance  equal  to  the  circular 
arc  ce,  as  the  arm  hp  swings  to  hr\  and  also  that  the 
distance  the  wheel  w  slides  on  the  arm  cd  does  not 
depend  on  its  position  on  the  arm;  it  is  true  that  the 
wheel  will  roll  further  if  it  is  more  remote  from  c,  but 
that  does  not  affect  the  reading. 

We  are  now  ready  to   consider  a   diagram   like 


9o 


THE   STEAM-ENGINE   INDICATOR. 


pqrs,  Fig.  63,  similar  to  Fig.  53  ,  page  78.  As 
before,  there  are  four  operations  to  consider:  (i)  the 
arm  hp  moves  parallel  to  itself,  and  the  wheel  meas- 
ures the  area  hpqi',  (2)  the  arm  lip  swings  through  the 
angle  qir,  and  the  wheel  records  the  distance  fg\  (3) 
the  arm  moves  parallel  to  itself,  and  the  wheel  meas- 
ures the  area  rihs]  and  (4)  the  arm  swings  through 


FIG.  63. 

the  angle  shp,  and  the  wheel  records  the  distance  ec. 
But  ec  is  equal  to  fg  and  is  recorded  in  the  contrary 
sense,  and  therefore  the  pivoting  about  i  and  the  piv- 
oting about  h  have  finally  no  influence  on  the  read- 
ing. The  instrument  records  the  difference  between 
the  areas  hpqi  and  hsri,  because  the  latter  is  measured 
in  contrary  direction,  or  is  subtracted,  which  gives 
the  area  of  the  figure  pqsr.  The  extension  of  the 
action  of  the  instrument  from  a  figure  like  pqrs  to  an 
irregular  figure  is  of  course  just  like  that  set  forth  on 
page  79. 

It  will  be  noted  now  that  the  arm  cd  may  be  placed 


THE  STEAM-ENGINE   INDICATOR.  9 1 

anywhere  along  the  arm  hp,  and  that  the  wheel  may 
have  any  diameter  without  affecting  the  action  of  the 
instrument.  The  wheel  should  be  truly  circular  or 
the  swinging  of  the  tracing-arm  back  and  forth  will 
not  have  equal  and  contrary  effects,  as  is  necessary 
for  the  proper  action  of  the  instrument. 

This  instrument  is  commonly  used  in  the  manner 
given  on  page  74  for  the  Amsler  planimeter,  Fig.  47 
and  Fig.  48;  that  is,  the  length  of  the  tracing-arm 
from  the  hinge  to  the  tracing-point  is  made  equal  to 
the  length  of  an  indicator  diagram,  and  consequently 
the  reading  of  the  planimeter  is  equal  to  the  mean 
width  of  the  diagram  in  inches,  or  in  pounds  per  inch, 
depending  on  the  graduation  of  the  paper  scale  inside 
the  glass  tube  (Fig.  59)  which  forms  the  arm  CD  of 
the  instrument.  Several  tubes,  with  two  scales  each, 
are  furnished  with  a  planimeter.  A  scale  of  inches 
and  tenths  can  be  used  for  measuring  the  width  of  a 
diagram  in  inches,  or  it  may  be  considered  to  be  a 
scale  of  ten  to  the  inch  for  reading  mean  effective 
pressures  directly;  other  scales  are  conveniently  ar- 
ranged for  various  indicator  springs. 

Through  the  hinge  of  this  planimeter  there  is  a 
style  that  is  retracted  by  a  spring,  but  it  can  be  thrust 
down  even  with  the  tracing-point  by  pressing  on  its 
head.  With  this  point  pressed  down  the  length  of 
the  tracing-arm  can  be  conveniently  made  equal  to 
the  length  of  the  diagram  when  it  is  desired  to  deter- 
mine the  mean  effective  pressure  of  an  indicator  dia- 


92  THE   STEAM-ENGINE   INDICATOR. 

gram.  If  the  area  of  a  diagram  is  desired,  the  length 
of  the  tracing-arm  can  be  set  by  direct  comparison 
with  a  scale  of  inches;  for  example,  the  arm  may  be 
made  four  inches  long  and  a  scale  of  fortieths  may  be 
used  for  measuring  areas  in  square  inches,  ten  forti- 
eths corresponding  to  one  square  inch;  or  the  arm 
may  be  made  five  inches  long  with  a  scale  of  fiftieths 
in  the  glass  tube. 

Horse-power  of  an  Engine. — Work  is  measured 
mechanically  in  foot-pounds,  and  can  be  calculated 
by  multiplying  the  force  which  does  the  work  by  the 
distance  through  which  that  force  is  exerted.  Thus, 
a  force  of  five  pounds  moved  through  a  distance  of 
ten  feet  will  generate  5  X  10  =  50  foot-pounds. 

Power  is  the  amount  of  work  done  in  a  unit  of 
time.  The  unit  of  power  for  engineering  purposes  is 
33,000  foot-pounds  per  minute.  Thus,  a  force  of 
2500  pounds  moving  at  the  rate  of  660  feet  per  min- 
ute will  generate. 

660  X  2500  ~  1,650,000  foot-pounds 
per  minute,  and  will  develop 

1,650,000  -r-  33,000  =  50  horse-power. 

To  find  the  horse-power  of  a  steam-engine: 

(1)  Take  indicator  diagrams  from  both  ends  of  the 
cylinder  and  determine  the  mean  effective  pressure 
of  each  separately. 

(2)  Ascertain  the  diameter  of  the  cylinder  and  of 


THE  STEAM-ENGINE  INDICATOR.  93 

the  piston-rod,  and  determine  the  area  of  the  piston 
and  of  the  section  of  the  piston-rod  in  square  inches. 
Subtract  the  area  of  the  piston-rod  from  the  area  of 
the  piston  to  find  the  net  area  of  the  crank  side  of  the 
piston. 

(3)  Multiply  the  area  of  the  piston  by  the  mean 
effective  pressure  from  the  head-end  diagram;  and 
multiply  the  net  area  of  the  crank  side  of  the  piston 
by  the  mean  effective  pressure  from  the  crank-end 
diagram;  add  the  two  products. 

(4)  Ascertain  the  stroke  of  the  piston  in  feet  and 
multiply  by  the  sum  obtained  under  (3),  and  by  the 
revolutions  of  the  engine  per  minute;  divide  by  33,- 
ooo,  and  the  final  result  will  be  the  horse-power  of 
the  engine. 

To  express  this  as  an  equation  let 

pi  and  /„  be  the  head-end  and  crank-end  mean  effec- 
tive pressures ; 
D  be  the  diameter  of  the  cylinder;   its  area  is 

3.I4I6/?1 


d  be  the  diameter  of  the  piston-rod ;  its  area  is 

3.1416^' 
4 

5  be  the  stroke  in  feet; 

R  be  the  revolutions  per  minute ; 


94  THE   STEAM-ENGINE  INDICATOR. 

.I4I6Z?8 


4  4 

Here  7//P  stands  for  indicated  horse-power. 

Instead  of  calculating  the  areas  of  the  piston  and 
piston-rod,  it  is  convenient  to  take  them  from  Table  I 
of  the  Appendix. 

If  the  engine  has  a  tail-rod,  the  area  of  its  section 
must  be  subtracted  from  the  area  of  the  piston  to 
get  the  net  area  of  the  head  side  of  the  piston. 

As  an  example,  we  will  make  the  calculation  for 
the  horse-power  of  an  engine  having  the  following 
dimensions: 

Diameter  of  cylinder  ................  1  6    inches 

Diameter  of  piston-rod  .............        2-J-       " 

Stroke  ............................        2     feet 

Revolutions  per  minute  ..............  130 

Head-end  mean  effective  pressure  .....  59.8  pounds 

Cranke-and  mean  effective  pressure..  .  .  59.2       " 

The  areas  of  the  piston  are: 

.    3.1416X16' 

Head  end,  -  =201.06  square  inches. 
4 


3.1416x6        . 
Crank  end,  --  --  ==  196.15  sq.  in. 
4  4 

The  horse-power  is 
{59-8  X  201.06  +"59.  2.X  196.15!  X  2  X  130-^33,000=  186.2. 


THE  STEAM-ENGINE  INDICATOR.  95 

Engine  Constant. — For  a  rough-and-ready  calcula- 
tion the  average  area  of  the  piston  may  be  multiplied 
by  the  average  mean  effective  pressure;  this  product 
may  now  be  multiplied  by  twice  the  stroke  in  feet  and 
by  the  revolutions  per  minute,  and  the  result  divided 
by  33,000.  This  method  applied  to  the  preceding  ex- 
ample will  give: 

Average  area  of  piston, 

3.1416X16'      I      3.1416X2.5' 

X =198.6  square  inches; 

424 

Average  mean  effective  pressure, 

4(59-8+  59-2)=  59-5; 
59.5  X  198.6  X  2  X  2  X  130  -f-  33,000  =  186.2. 

Had  the  mean  effective  pressures  been  more  unlike 
the  error  would  be  important. 

When  this  method  is  used  -it  is  customary  to  unite 
all  the  factors  except  the  average  mean  effective  pres- 
sure into  a  constant  called  the  engine  constant. 

The  engine  constant  for  the  case. in  hand  is 

198.6  X  2  X  2  X  130  -7-  33>ooo  =  3.13, 

and  the  horse-power  for  the  average  mean  effective 
pressure  given  above  is 

59-5  X  3.131  =  186.2. 

Piston-displacement. — The  piston-displacement  of 
an  engine  is  obtained  by  multiplying  the  area  of  the 


96  THE   STEAM-ENGINE   INDICATOR. 

piston  in  square  feet  (allowing  for  the  piston-rod  at 
the  crank  end)  by  the  stroke  in  feet. 

For  example,  the  piston-disp'acement  of  the  engine 
mentioned  above  may  be  found  as  follows: 

Area  piston  : 

head  end   =  201. 06 -^  144=  1.3965  square  feet ; 

crank  end  =   196. 1 5  -f-  144  =  1 .362 1  square  feet. 
Piston-displacement : 

head  end   =   1.3965  X  2       =  2.7930  cubic  feet; 

crank  end  =  1.3621  X  2       =  2.7242  cubic  feet. 

The  term  piston-displacement  means  the  space  dis- 
placed by  the  piston;  the  meaning  is  most  evident  for 
a  pump,  which  should  displace  or  force  out  a  volume 
of  water  equal  to  the  piston-displacement  for  each 
stroke  of  the  pump-piston,  provided  that  there  is  no 
leakage  and  the  valve  action  is  perfect.  The  configu- 
ration of -the  piston,  whether  it  is  flat,  conical,  or  with 
protruding  'boss  or  nuts,  does  not  affect  the  piston- 
displacement.  A  compressed-air  engine  will  take  its 
piston-displacement  of  air  per  stroke,  provided  that 
its  valve  gives  free  passage  of  air  and  allows  the  air 
to  enter  till  the  stroke  is  completed;  if  the  cut-off  for 
such  an  engine  is  at  half-stroke,  then  it  will  take  half 
of  its  piston-displacement  per  stroke.  This  state- 
ment for  an  air-engine  ignores  the  effect  of  waste 
space  at  the  end  of  the  cylinder  and  the  effect  of  com- 
pression. A  steam-engine  cannot  have  its  steam  con- 


THE  STEAM-ENGINE  INDICATOR.  97 

sumption  calculated  in  so  simple  a  manner  because 
much  of  the  steam  admitted  is  condensed  on  the  walls 
of  the  cylinder;  during  the  expansion,  and  especially 
during  the  exhaust,  this  condensed  steam  is  re- 
evaporated.  A  complete  understanding  of  cylinder 
condensation  and  its  effect  on  the  economy  of  a 
steam-engine  can  be  obtained  only  by  an  extended 
study  of  the  thermal  theory  of  the  steam-engine,  and 
of  tests  on  steam-engines;  an  introduction  to  this 
interesting  subject  can  be  obtained  here  by  making 
calculations  of  the  indicated  steam  consumption  of 
a  steam-engine. 

Clearance. — The  waste  space  in  the  steam-passage 
leading  to  the  cylinder,  and  between  the  cylinder- 
head  and  the  piston  when  the  latter  is  at  the  end  of 
its  stroke,  is  called  the  clearance  of  the  engine.  This 
clearance  is  sometimes  given  in  cubic  inches  or  cubic 
feet,  but  is  more  commonly  given  as  a  percentage  of 
the  piston-displacement.  The  clearance  here  dis- 
cussed must  not  be  confused  with  the  machinist's 
clearance,  or  distance  in  fraction  of  an  inch,  between 
the  piston  and  the  cylinder-head. 

If  the  clearance  of  the  engine  discussed  above  is 
0.279  of  a  cubic  foot,  it  is  said  to  have  10%  clearance. 

Absolute  Pressure. — The  indicator  shows  the  pres- 
sure in  the  cylinder  of  an  engine  measured  from  the 
atmospheric  line,  or  the  pressure  above  the  pressure 
of  the  atmosphere.  A  pressure  less  than  that  of  the 
atmosphere  is  commonly  called  a  vacuum;  such  a 


98  THE   STEAM-ENGINE   INDICATOR. 

vacuum  is  measured  downwards  from  the  atmos- 
phere in  pounds,  on  an  indicator  diagram.  In  much 
the  same  way  boiler-pressures  are  measured  by  steam- 
gauges  above  the  atmosphere.  On  the  other  hand, 
a  vacuum  in  a  condenser  is  measured  by  a  vacuum 
gauge,  or  by  a  U  tube  filled  with  mercury,  in  inches 
of  mercury. 

To  convert  a  pressure  (or  vacuum)  in  inches  of 
mercury  to  pounds,  multiply  by  0.49.  Thus  a  vacuum 
of  25  inches  corresponds  to  a  pressure  of 

25  X  49  =  I2j 

pounds  below  the  atmosphere. 

The  pressure  of  the  atmosphere  is  to  be  obtained 
by  aid  of  a  barometer.  For  the  greater  part  of  engi- 
neering work  the  pressure  of  the  atmosphere  may  be 
taken  at  30  inches  of  mercury,  or  14.7  pounds. 

The  real  pressure  measured  from  an  absolute 
vacuum  is  obtained  by  adding  the  pressure  by  a 
gauge,  or  by  the  indicator,  to  the  pressure  of  the 
atmosphere.  A  pressure  measured  on  an  indicator 
diagram  below  the  atmospheric  line  is  to  be  sub- 
tracted from  the  pressure  of  the  atmosphere  to  get 
the  corresponding  absolute  pressure.  And  in  like 
manner  a  vacuum  measured  by  a  vacuum  gauge  is 
to  be  reduced  to  pounds  and  subtracted  from  the 
pressure  of  the  atmosphere  to  get  the  absolute  pres- 
sure. 

Absolute  pressures  are  used  in  all  the  theoretical 


THE   STEAM-ENGINE   INDICATOR.  99 

discussions   and   calculations   of  steam,   vapors,  and 
gases,  and  in  tables  of  the  properties  of  steam. 

Temperature. — For  engineering  purposes  it  is  cus- 
tomary to  measure  temperatures  by  the  Fahrenheit 
scale,  which  has  the  freezing-point  of  water  at  32°  F. 
and  the  boiling-point  at  212°  F. 

Absolute  Temperatures. — In  computations  for  air 
and  other  gases  it  is  convenient  to  use  absolute  tem- 
peratures, which  are  obtained  by  adding  460°. 7  to 
temperatures  on  the  Fahrenheit  scale.  For  example, 
the  absolute  temperature  of  freezing-point  is  32°  + 
4607  =  492°7- 

Pressures. — It  is  customary  to  measure  pressures  in 
pounds  on  the  square  inch,  but  for  certain  calcula- 
tions it  is  convenient  to  take  pressures  in  pounds  on 
the  square  foot;  this  gives  what  is  called  the  specific 
pressure.  The  specific  pressure  is  consequently  144 
times  the  pressure  in  pounds  on  the  square  inch. 

Density. — The  weight  of  a  cubic  foot  of  any  sub- 
stance is  called  its  density.  For  example,  one  cubic 
foot  of  water  at  32°  F.  weighs  62.4  pounds. 

The  densities  of  several  gases  at  32°  F.  and  at  at- 
mospheric pressure  are: 

Air   0.08070     pounds 

Nitrogen    0.07839          " 

Oxygen    0.08923          " 

Hydrogen    0.005590        " 

Carbonic  acid 0.1234  " 


100  THE   STEAM-ENGINE   INDICATOR. 

Specific  Volumes.  —  The  volume  occupied  by  one 
pound  of  a  substance  is  called  the  specific  volume.  It 
is  the  reciprocal  of  the  density;  that  is,  it  can  be  calcu- 
lated by  dividing  i  by  the  density.  The  specific  vol- 
umes of  ordinary  gases  are: 

Air    .........................  I2-39  cubic  feet 

Nitrogen    ....................  12.76 

Oxygen   .....................  11.21 

Hydrogen    ...................  I7&-9 

Carbonic  acid  .................       8.  103 

Properties  of  Gases.  —  The  following  simple  equation 
allows  us  to  calculate  the  properties  of  gases: 


T'       T0  ' 

where  p,  v,  and  T  represent  the  pressure,  volume,  and 
temperature,  while  />0,  VQ,  and  T0  are  the  standard 
conditions;  that  is, 

p0  =  pressure  of  the  atmosphere; 

T0  =  absolute  temperature  of  freezing-point  = 

492.7; 

Nonspecific  volume  at  p0  and  T0. 
The  use  of  this  equation  can  be  best  illustrated  by 
an  example.     Suppose  that  air  in  a  certain  reservoir 
or  cylinder  has  a  pressure  of  92  pounds  above  the  at- 
mosphere and  a  temperature  of  70°  F.,  so  that 
/  =  92  +    14.7  =  106.7, 
T=  70  +  460.7  =  530.7, 


THE  S  TEA  M-ENGINE  lNJ?I<*A  if  tf  J?/ ;  \>\ J  \O  1 
and 

106.7  X  v  _  H-7  X  12.39 
530.7~  492-7 

I4.7XI2.39X5307  =  1<g       cubic  feet> 
492.7  X  106.7 

The  corresponding  density  or  weight  per  cubic 
foot  is  0.5439  pounds. 

Calculated  Air-consumption. — If  we  know  the  pis- 
ton-displacement of  a  compressed-air  engine,  the  air- 
pressure,  and  the  speed,  the  amount  of  air  can  be  cal- 
culated with  a  fair  degree  of  approximation. 

It  can  be  shown  that  a  compressed-air  engine  hav- 
ing a  diameter  of  13^  inches  and  a  stroke  of  2  feet  will 
develop  about  100  horse-power,  provided  that  it 
makes  150  revolutions  per  minute  and  is  supplied 
with  air  at  92  pounds  pressure  by  the  gauge  and  at 
70°  F.,  the  cut-off  being  at  quarter-stroke. 

If  the  diameter  of  the  piston-rod  is  two  inches,  the 
average  piston-displacement  will  be  1.974  cubic  feet. 
If  the  clearance  and  compression  are  neglected  the 
engine  will  use  an  average  volume  of 

V4  X  1.974  =  4935  cubic  feet 

of  air  per  stroke.    The  weight  of  air  per  stroke  (using 
the  result  of  the  preceding  problem)  will  be 

4935  X  .5439  =  0.268 


TfTE   STEAM-ENGINE  INDICATOR. 

pounds.  The  engine  makes  150  revolutions  per  min- 
ute, or  2  X  150  strokes,  and  consequently  will  use 

2  X  150  X  0.263  =  80.4 
pounds  per  minute,  or 

60  X  80.4  =  4820 

pounds  per  hour;  so  that  the  air-consumption  per 
horse-power  per  hour  will  be  48.2  pounds,  the  engine 
being  assumed  to  develop  100  horse-power.  Taking 
account  of  compression  and  clearance  will  give  about 
one-tenth  larger  consumption.  But  since  this  calcula- 
tion is  put  in  for  sake  of  illustration,  the  method  of 
allowing  for  clearance  and  compression  need  not  be 
given  at  length. 

Properties  of  Steam. — The  properties  of  saturated 
steam  determined  by  experiments  and   calculations 
vary  in  so  complex  a  manner  that  it  is  customary  to 
take  them  from  a  table.    The  Appendix  gives  a  brief 
table  (Table  II);  more  complete  and  extensive  tables, 
together  with  tables  of  properties  of  other  vapors, 
will  be  found  in  various  works  on  thermodynamics 
or  in  the  author's  Tables  of  Properties  of  Saturated 
Steam,  etc.    The  properties  are: 
/>,  the  absolute  pressure  in  pounds  per  square  inch; 
t,  the  temperature  in  degrees  Fahrenheit; 
q,  the  heat  of  the  liquid,  that  is,  the  heat  required  to 

raise  the  temperature  of  a  pound  of  water  from 

32°  to  the  temperature  t°  F.; 


THE   STEAM-ENGINE   INDICATOR,  IO3 

h,  the  total  heat,  or  the  heat  required  to  raise  a  pound 
of  water  from  32°  to  the  temperature  t°  F.,  and 
to  vaporize  it  against  the  corresponding  pres- 
sure />; 

r,  the  heat  of  vaporization,  or  the  heat  required  to 
vaporize  a  pound  of  water  against  the  pressure 
p  after  it  has  been  raised  to  the  temperature 
f°F.; 

v,  the  volume  of  one  pound  of  steam; 
d,  the  weight  of  one  cubic  foot  of  steam. 

Indicated  Steam-consumption. — A  calculation  is 
sometimes  made  of  the  steam-consumption  of  an  en- 
gine by  a  method  like  that  briefly  illustrated  above 
for  finding  the  air-consumption  for  a  compressed-air 
engine.  The  actual  steam-consumption  is  often  half 
again  as  much  as  the  calculated  consumption  because 
there  is  likely  to  be  a  considerable  weight  of  water  in 
the  cylinder  in  addition  to  the  steam.  This  inter- 
feres with  the  direct  usefulness  of  making  calcula- 
tions of  steam-consumption  from  indicator  diagrams. 
Nevertheless  such  calculations  are  customary  and 
have  certain  interesting  features.  The  following  ex- 
ample wi1!  illustrate  the  process. 

A  small  Corliss  engine  in  the  laboratory  of  the 
Massachusetts  Institute  of  Technology  has  the  fol- 
lowing dimensions: 

Diameter  of  cylinder 8.12  inches 

D;ameter  of  piston-rod 1.5         " 

Stroke  2        feet 


104  THE  STEAM-ENGINE   INDICATOR. 

Piston-displacement:  crank  end...   0.6791  cubic  feet 

head  end.  .  .   0.7016 

Clearance  in  per  cent  of  displacement:  crank  end. 3. 72 

head  end.  .5.42 

A  test  on  this  engine  gave  the  following  data  and 
results: 

Boiler-pressure  above  the  atmosphere  .  .    71.9  poun  Is 

Pressure  of  atmosphere 14.8       " 

Pressure  at  cut-off:  crank  end 57.8       " 

head  end 57.3       " 

Pressure  at  release:  crank  end 5.9       " 

head  end 14.2       " 

Pressure  at  compression:  crank  end  ....     4.1 

head  end 4.0       " 

Cut-off:  crank  end 0.19     of  stroke 

head  end 0.29 

Release:  crank  end    0.950 

head  end    0.960 

Compression:  crank  end 02 

head  end 0.03  " 

Mean  effective  pressure:  crank  end..   26.92  pounds 

head  end    .  .    37.27       " 
Revolutions  per  minute   60.36 

When  cut-off  occurred  at  the  crank  end  the  piston 
was  0.19  of  the  stroke  from  the  beginning,  and  the 
volume  developed  by  the  piston  was 

0.19  X  0.6791  —  0.12903 


THE   STEAM-ENGINE  INDICATOR.  IO$ 

of  a  cubic  foot;  but  the  clearance  is  3.72  per  cent  of 
the  piston-displacement,  and  added  the  volume 

0.0372  X  0.6791  —  0.02526 

of  a  cubic  foot,  giving  a  total  of  0.1526  of  a  cubic  foot 
to  be  filled  with  steam  at  cut-off.  Another  way  of 
finding  this  same  quantity  is  to  add  the  clearance 
directly  to  the  cut-off,  giving  for  the  volume 

(0.194-0.0372)0.6791  =  0.1543  cubic  foot. 
The  absolute  pressure  at  cut-off  is 

57.8  +  14.8  =  72.6  pounds. 

From  the  table  of  properties  of  steam  in  the  Appen- 
dix it  appears  that  one  cubic  foot  of  steam  at  72.6 
pounds  pressure  weighs  0.1684  of  a  pound.  Conse- 
quently the  weight  of  steam  in  the  cylinder  at  cut-off 
for  the  crank  end  was 

0.1543  X  0.1684  —  0.02598  of  a  pound. 

A  similar  calculation  for  the  weight  of  steam  at  re- 
lease of  the  crank  end  gives  for  the  volume  of  steam 
in  the  cylinder 

(0.95  +  0.0372)  0.6791  =  0.6705 
of  a  cubic  foot;  at  release  the  absolute  pressure  is 

5.9  +  14-8  =  20.7 
pounds,   at  which  pressure  a   cubic   foot  of  steam 


106  THE   STEAM-ENGINE  INDICATOR. 

weighs  0.05188  of  a  pound,  so  that  the  weight  of 
steam  at  release  appears  to  be 

0.05188  X  0.6705  =  0.0348 
of  a  pound. 

Again,  we  have  for  the  volume  in  the  cylinder  at 
compression  for  the  crank  end 

(0.02  +  0.0372)  0.6791  =  0.0388 

of  a  cubic  foot;  the  absolute  pressure  at  compres- 
sion is 

4.1  +  14.8  =  18.9 

pounds,  at  which  one  cubic  foot  of  steam  weighs 
0.04762  of  a  pound,  so  that  the  steam  caught  and 
saved  in  the  cylinder  at  compression  weighs 

0.0388  X  0.04762  =  0.0018 
of  a  pound. 

The  same  sort  of  a  calculation  for  the  head  end 
gives  the  following  results: 
Weight  of  steam 

at  cut-off,  head  end .     0.0405  of  a  pound 

at  release 0.0507  " 

at  compression   ....   0.0028 

The  average  for  the  two  ends  gives  for  the  steam 
in  the  cylinder 

at  ct  t-off 0.0332  of  a  pound 

at  release 0.0422 

at  compression   ....  0.0023          " 


THE   STEAM-ENGINE  INDICATOR.  IO/ 

The  steam  used  by  this  engine  during  the  test  was 
condensed,  collected,  and  weighed;  it  amounted  to 
0.0621  of  a  pound  per  stroke.  Now  there  is  good 
reason  to  consider  that  there  is  no  water  in  the  cylin- 
der at  the  end  of  the  exhaust,  as  there  is  abundant 
opportunity  for  evaporation  during  the  exhaust;  con- 
sequently we  may  consider  that  there  is  nothing  but 
steam  in  the  cylinder  at  compression.  Adding  this 
amount  to  the  steam  exhausted  from  the  engine  gives 

0.0621  +  0.0023  =  0.0644  pounds 

for  the  average  weight  of  steam  in  the  cylinder  of  the 
engine  before  release  occurred. 

If  the  steam  calculated  from  the  pressure  at  cut-off 
is  compared  with  the  sum  just  obtained,  it  appears 
that  of  the  substance  in  the  cylinder  at  cut-off 

0.0332 

X  I0°  ==  52  per  cent 


is  steam  and  46  per  cent  is  water.    In  like  manner  it 
appears  that  there  is 

0.0422 

—  ^—  x  ioo  =  66 

0.0644 

per  cent  of  steam  and  34  per  cent  of  water  at  release. 
The  proportion  of  water  and  steam  in  the  cylinder 
of  an  engine  either  at  cut-off  or  release  depends  on 
the  size,  style,  and  manner  of  running  the  engine. 
This  same  engine  when  developing  4  horse-power 
with  the  cut-off  at  5  per  cent  of  the  stroke  showed 


IO8  THE   STEAM-ENGINE   INDICATOR 

only  33  per  cent  of  steam  at  cut-off;  again,  when 
using  steam  at  58  pounds  above  the  atmosphere  and 
with  cut-off  at  69  per  cent  of  the  stroke,  there  was  72 
per  cent  of  steam  at  cut-off  and  76  at  release.  Larger 
engines  are  likely  to  show  a  larger  proportion  of 
steam  than  do  small  engines;  superheating  also  re- 
duces the  amount  of  water  in  the  cylinder  at  both  cut- 
off and  release;  steam-jackets  have  a  similar  effect, 
and,  especially  when  applied  to  compound  engines, 
may  give  dry  steam  at  release  from  the  low-pressure 
cylinder.  The  study  of  cylinder  condensation  and  re- 
evaporation  of  steam-engines  is  one  of  the  most  in- 
teresting subjects  for  the  steam-engineer,  but  it  is 
much  too  extensive  to  be  printed  here. 

Returning  to  our  calculation,  it  appears  that  the 
indicator  shows  0.0348  of  a  pound  of  steam  in  the 
crank  end  of  the  cylinder  at  release,  and  0.0018  of  a 
pound  at  compression.  The  calculated  weight  of 
steam  exhausted  may  be  considered  to  be 

0.0348  —  0.0018  =  0.0330 

of  a  pound.  In  like  manner  the  head  end  has  0.0507 
of  a  pound  at  release  and  0.0028  of  a  pound  at  com- 
pression, so  that  the  calculated  exhaust  from  the 
head  end  of  the  cylinder  will  be 

0.0507  —  0.0028  =  0.0479 

of  a  pound.  The  sum  of  these  quantities  may  be  taken 
for  the  exhaust  per  revolution,  giving 

0.0330  +  0.0479  =  0.0810 


THE   STEAM-ENGINE   INDICATOR.  109 

of  a  pound.  The  engine  made  60.36  revolutions  per 
minute,  consequently  the  steam  exhausted  per  hour 
was 

60  X  60.36  X  0.0810  =  293 

pounds.  The  horse-power  calculated  from  the  dimen- 
sions of  the  cylinder  and  the  mean  effective  pressures 
is  11.7;  so  that  the  calculated  steam-consumption  per 
horse-power  per  hour  is 

293--  11.7  =  25 

pounds.  On  the  other  hand,  the  actual  steam-con- 
sumption from  the  weight  of  steam  condensed  and 
weighed  in  an  hour  was  37  pounds.  It  is  well  to  re- 
call what  was  laid  down  in  the  first  paragraph  of  this 
book,  namely,  that  the  indicator  shows  only  the  pres- 
sure of  the  steam  in  the  cylinder.  The  so-called  indi- 
cated steam-consumption  of  an  engine  is  likely  to  be 
seriously  in  error  because  it  does  not  and  cannot  take 
account  of  the  water  in  the  cylinder,  which  at  release 
is  liable  to  be  as  much  as  one-third  of  the  working 
substance  in  the  cylinder.  When  a  test  of  an  engine 
has  been  made  and  the  actual  steam-consumption  has 
been  determined,  a  calculation  of  the  proportions  of 
steam  and  water  in  the  cylinder  at  cut-off  and  release 
is  instructive,  as  it  gives  some  idea  of  the  influence  of 
the  cylinder  walls  on  the  action  of  the  steam.  When 
sufficient  observations  are  taken  during  a  test,  it  is 
possible  to  determine  more  exactly  the  influence  of 
the  cylinder  walls  by  aid  of  an  analysis  proposed  by 
Hirn;  thus  a  test  on  the  engine  under  consider- 


HO  THE   STEAM-ENGINE  INDICATOR. 

ation  when  running  under  nearly  the  same  con- 
ditions and  developing  n.i  horse-power  showed 
that  of  the  heat  supplied  to  the  cylinder  by  the' 
entering  steam  37  per  cent  was  absorbed  by  the 
cylinder  walls  during  the  admission  up  to  cut- 
off, that  17  per  cent  was  returned  by  the  walls 
during  expansion,  and  that  15  per  cent  was  thrown 
out  from  the  walls  during  exhaust;  the  last  quantity, 
called  exhaust  waste,  plays  an  important  part  in  the 
discussion  of  the  losses  of  the  steam-engine. 

Steam  per  Horse-power  per  Hour. — A  common  way 
of  stating  the  performance  of  a  steam-engine  is  to 
give  the  steam-consumption  in  pounds  per  horse- 
power per  hour.  The  horse-power  is  habitually  de- 
termined by  aid  of  the  indicator,  which  affords  the 
means  of  calculating  the  power  developed  in  the  cylin- 
der. The  steam  may  be  determined  by  condensing  it 
in  a  surface  condenser  and  collecting  and  weighing  it; 
or  if  the  engine  is  supplied  from  a  boiler,  or  a  battery 
of  boilers,  which  is  used  for  that  purpose  only,  the 
feed-water  supplied  to  the  boilers  can  be  weighed  or 
measured.  In  either  case  the  test  gives  the  means  of 
calculating  the  steam  used  by  the  engine  per  hour, 
which  may  be  divided  by  the  horse-power  to  find  the 
steam  per  horse-power  per  hour. 

This  method  of  stating  steam-engine  performance 
is  open  to  criticism  because  the  amount  of  heat  re- 
quired to  evaporate  water  depends  on  the  tempera- 
ture of  the  feed-water  supplied  to  the  boiler  and  on 


THE   STEAM-ENGINE   INDICATOR.  Ill 

the  pressure  under  which  the  steam  is  evaporated. 
To  exhibit  this,  consider  first  the  effect  of  supplying 
the  feed-water  to  a  boiler  at  102°  F.  and  evaporating 
it  at  61.3  pounds  by  the  gauge  (76  pounds  absolute), 
as  compared  with  supplying  feed-water  at  212°  to  the 
same  boiler.  Now  the  heat  of  the  liquid  at  102°  F.  is 
70  thermal  units,  and  at  76  pounds  pressure  the  heat 
of  the  liquid  is  277.8  thermal  units,  while  the  heat  of 
vaporization  at  76  pounds  is  898.2;  consequently  the 
heat  required  to  raise  water  from  100°  F.  and  bring  it 
up  to  boiling  at  76  pounds  pressure  is 

277.8  —  70  =  207.8 

thermal  units,  and  the  heat  required  to  heat  it  and 
vaporize  it  is 

207.8  +  892.2  =  1106 

thermal  units;  again,  the  heat  required  to  raise  the 
water  from  212°  F.  to  boiling  temperature  at  76 
pounds  is 

277.8  —  180.8  +  898.2  =  995.2 

thermal  units,  the  heat  of  the  liquid  at  212°  F.  being 
180.8.  The  difference  in  this  case  is  about  eleven 
per  cent.  Again,  consider  the  effect  of  carrying  135.3 
pounds  by  the  gauge  (150  absolute)  instead  of  61.3 
pounds  by  the  gauge.  The  heat  of  the  liquid  at  150 
pounds  absolute  is  330,  and  the  heat  of  vaporization  is 
861.2,  so  that  the  heat  required  to  vaporize  one  pound 
of  water  from  100°  F.  is 

33°  —  7°  +  861.2  =  1 121.2, 


112  THE   STEAM-ENGINE   INDICATOR. 

consequently  the  effect  of  raising  the  pressure  is 
about  one  and  a  half  per  cent. 

When  part  of  the  steam  is  supplied  to  the  cylinder 
of  an  engine  and  part  is  used  in  a  steam-jacket  from 
which  the  condensation  is  returned  directly  to  the 
boiler,  the  inadequacy  of  reporting  steam-consump- 
tion in  pounds  per  horse-power  per  hour  is  even  more 
marked. 

Thermal  Unit. — Heat  may  be  measured  in  British 
thermal  units  (B.  T.  u.);  the  thermal  unit  being  de- 
fined as  the  heat  required  to  raise  one  pound  of  water 
from  62°  F.  to  63°  F.  The  properties  of  saturated 
steam,  such  as  heat  of  the  liquid,  heat  of  vaporization, 
and  total  heat,  are  given  in  thermal  units. 

Thermal  Units  per  Horse-power  per  Minute. — To 
avoid  the  ambiguity  of  stating  engine  performance  in 
pounds  of  steam  per  horse-power  per  hour  engi- 
neers resort  to  the  expedient  of  using  thermal  units 
per  horse-power  per  minute.  This  method  is  best 
presented  by  an  example. 

Referring  to  the  calculation  of  indicated  steam-con- 
sumption we  find  that  the  engine  when  developing 
11.7  horse-power  used  37  pounds  of  steam  per  horse- 
power per  hour,  with  a  boiler-pressure  of  71.9  pounds 
by  the  gauge,  or,  allowing  14.8  pounds  for  the  atmos- 
phere, of  86.7  pounds  absolute.  With  an  exhaust 
feed-water  heater  the  feed-water  for  a  boiler  supplying 
steam  to  a  non-condensing  engine  may  be  raised  to 
212°  F.  The  heat  of  the  liquid  at  212°  F.  is  180.8 


THE  STEAM-ENGINE  INDICATOR.  1 13 

B.  T.  u.,  the  heat  of  the  liquid  at  86.7  pounds  absolute 
is  287.3  B.  T.  u.,  and  the  heat  of  vaporization  is  891.2 
B.  T.  u.  The  heat  required  to  heat  the  water  from 
212°  F.  to  a  pressure  of  86.7  pounds  was 

287.3  --  180.8  =  106.5  B.  T.  u. 

Now  it  appeared  from  a  calorimeter  test  of  the 
steam  supplied  to  the  engine  that  it  contained  two  per 
cent  of  water;  consequently  the  heat  required  to  va- 
porize 0.98  of  a  pound  of  steam  was 

0.98  X  891.2  =  873.4  B.  T.  u. 

The  heat  required  to  form  a  pound  of  steam  from 
a  pound  of  water  was  consequently 

106.5  +  873-4  =  979-9  B-  T-  u- 

The  engine  used  37  pounds  of  steam  per  hour  or 
37  -r-  60  pounds  per  minute,  and  consequently  it  re- 
quired 

979.9  X  37  -r-  60  =  604  B.  T.  u. 

per  horse-power  per  minute. 

When  an  engine  has  a  steam-jacket  the  steam  sup- 
plied to  the  jacket  must  be  determined  separately,  and 
the  thermal  units  for  the  jacket  are  to  be  calculated 
separately  and  added  to  the  thermal  units  for  the  cyl- 
inder. 


114  THE   STEAM-ENGINE   INDICATOR. 

Hyperbola. — It  is  sometimes  interesting  to  com- 
pare the  expansion  line  of  an  indicator  diagram  with 
some  regular  curve  of  the  same  general  character. 
The  curve  commonly  chosen  for  this  purpose  is  called 
the  rectangular  hyperbola;  this  curve  is  easily  drawn 
and  it  agrees  fairly  well  with  the  expansion  line  of 
many  large  engines  of  good  type.  In  the  design  of  a 
new  engine  it  is  customary  to  use  the  hyperbola  for 
the  expansion  line  in  laying  out  the  probable  indi- 
cator diagram. 

The  method  of  drawing  the  hyperbola  is  shown  by 
Fig.  64,  which  represents  a  diagram  taken  from  the 


O         0.1      0.2      0.3      0.4      0.5      0.6      0.7      0.8      0.9      1.0  V 
FlG.   64. 


high-pressure  cylinder  of  a  triple-expansion  engine  at 
the  Massachusetts  Institute  of  Technology.  In  the  first 
place  the  diagram  is  referred  to  the  axes  OP  and  0V 
of  no  volume  and  no  pressure.  For  this  purpose  lines 


THE   STEAM-ENGINE   INDICATOR.  11$ 

are  drawn  at  ab  and  cd  which  are  perpendicular  to  the 
atmospheric  line  and  which  touch  the  diagram  at  its 
ends.  Then  st  is  laid  off  equal  to  the  pressure  of  the 
atmosphere  (14.7  pounds),  and  OFis  drawn  parallel  to 
the  atmospheric  line.  Pressures  measured  from  0V 
are  consequently  absolute  pressures.  From  b  the  dis- 
tance Ob  is  laid  off  equal  to  the  length  of  the  diagram 
multiplied  by  the  clearance  in  per  cent  of  the  piston- 
displacement,  and  OP  is  drawn  perpendicular  to  OF; 
distances  measured  from  OP  along  the  axis  OF  are 
proportional  to  the  volumes  in  the  cylinder,  including 
clearance.  This  construction  may  be  conveniently 
made  by  laying  a  scale  across  the  diagram  so  that 
the  zero  shall  come  on  the  line  dc  produced,  and  the 
one  hundredth  division  shall  come  on  the  line  ba,  and 
then  the  clearance  (.09)  can  be  read  directly  from  the 
scale  beyond  the  one-hundredth  division.  Draw  a  line 
rs  through  the  point  of  release;  if  the  release  is  not  well- 
marked  a  point  near  release  may  be  chosen  at  ran- 
dom. Divide  the  distance  Ot  into  a  convenient  num- 
ber of  equal  parts,  ten  for  example;  draw  lines  at  the 
points  thus  located  and  number  them  as  shown. 
Measure  the  absolute  pressure  tr  at  release;  on  the 
diagram  the  pressure  is  30  pounds.  To  find  a  point  of 
the  curve  on  a  given  line  divide  the  pressure  at  r  by 
the  number  of  the  line  expressed  as  a  decimal  as  indi- 
cated on  the  diagram.  For  example,  the  pressure  on 
the  ninth  line  is  30  -=-  0.9  =  33.3  pounds.  The  pres- 
sures on  the  several  lines  are'. 


THE   STEAM-ENGINE   INDICATOR. 


30  -7-  0-9  = 

30  -f-  0.8  = 
30  ~  0.7  = 
30  -f-  0.6  = 
30  -H  0.5  = 
30  +  0.4  = 


33.3  pounds 
37-5   " 
42.7 

50.0  " 
60.0  " 
75-0 


30  -j-  0.3  =  100.0 

30  -4-  0.2  =  150.0 


Sometimes  the  hyperbola  is  drawn  from  a  point  at 
or  near  cut-off  as  shown  by  Fig.  65. 


FIG.  65. 

In  such  case  after  the  axes  0V  and  OP  are  drawn  a 
line,  as  ef,  can  be  drawn  at  or  near  cut-off,  and 
spaces  equal  to  Of  can  be  laid  off  as  shown  with  half 
or  quarter  spaces  if  necessary.  The  pressure  on  any 
line  can  be  found  by  dividing  the  pressure  at  cut-off 
by  the  number  of  the  line  expressed  as  a  whole  num- 
ber. For  example,  the  pressure  on  the  ordinate  2.\  is 

125 

-.-  50  pounds. 


THE  STEAM-ENGINE  INDICATOR. 


117 


The  hyperbola  drawn  on  the  diagram  Fig.  64  from 
the  point  of  release  rises  above  the  expansion-line; 
small  steam-engines  are  likely  to  give  diagrams  on 
which  the  hyperbola  will  rise  even  higher  above  the 
expansion-line;  large  steam-engines  with  steam-jack- 
ets may  give  diagrams  on  which  the  hyperbola  will 
cut  into  the  expansion  line  as  shown  by  Fig.  66, 


FIG.  66. 

which  is  a  diagram  taken  from  a  pumping-engine 
at  the  Chestnut  Hill  Station,  Boston  Water  Works. 

After  the  relation  of  the  hyperbola  to  the  expansion- 
line  of  the  diagram  from  an  engine  has  been  well  es- 
tablished some  defects  of  the  'engine  may  be  inferred 
from  drawing  the  hyperbola  on  a  diagram  which 
has  such  a  defect.  For  example,  a  leak  through 
an  admission-valve  will  tend  to  keep  up  the  pressure 
and  prevent  the  expansion-line  from  falling  as  rapidly 
as  it  should;  in  such  case  the  hyperbola  will  rise 
rapidly  away  from  the  expansion-line  when  'drawn 
from  a  point  at  release.  If  the  exhaust-valve  leaks 
a  contrary  effect  will  be  produced  and  the  expansion- 
line  will  fall  too  rapidly. 


Il8  THE  STEAM-ENGINE  INDICATOR. 

Oscillations  in  Diagrams. — Diagrams  taken  from  an 
engine  with  high  speed  of  rotation  are  likely  to  be  de- 
ranged by  oscillations  of  the  piston  and  pencil-motion, 
as  shown  by  Fig.  67,  which  was  taken  from  a  Porter- 
Allen  engine  making  350  revolutions  per  minute. 


FIG.  67. 

On  this  diagram  it  is  difficult  to  determine  the 
point  of  cut-off,  and  individual  measurements  of  pres- 
sure are  liable  to  large  errors;  the  mean  effective 
pressure  and  the  horse-power  calculated  from  it  are 
not  likely  to  be  affected  by  much  error  on  account  of 
the  oscillations;  all  diagrams  from  very  high-speed 
engines,  whether  or  not  they  are  deranged  by  oscilla- 
tions, are  liable  to  have  larger  errors  than  diagrams 
from  slow-speed  engines. 

Piston-friction. — Even  if  an  indicator  is  in  perfect 
condition  when  put  onto  an  engine  it  is  likely  to  be- 
come fouled  by  burnt  oil  or  other  material  from  the 
c}4inder  of  the  engine,  which  will  cause  excessive 
friction  of  the  indicator  piston.  Fig.  68  shows  a  dia- 


THE  STEAM-ENGINE  INDICATOR. 

gram  which  is  slightly  affected  by  piston-friction. 
The  steam-line  is  suspiciously  straight,  but  that  alone 
might  not  show  excessive  friction;  the  successive 


FIG.  68. 

steps  in  the  expansion-line  are,  however,  conclusive 
evidence  of  friction  of  the  piston.  This  diagram  was 
taken  from  a  slow-speed  engine,  so  that  oscillations 
are  not  to  be  expected. 

Fig.  69,  which  was  taken  from  a  locomotive,  shows 


FIG.  69. 

an  excessive  amount  of  piston-friction.  The  right- 
hand  diagram  is  the  normal  diagram  from  one  end  of 
the  cylinder,  and  the  smooth  diagram  at  the  left  is 


120  THE   STEAM-ENGINE   INDICATOR. 

the  normal  diagram  from  the  other  end.  When  the 
indicator  was  started  the  piston  came  up  under  the 
sudden  application  of  pressure,  but  stuck  fast  before 
it  had  come  to  the  top  of  the  diagram;  the  pencil  then 
drew  a  straight  line  with  the  piston  stuck  fast  till  the 
fall  of  pressure  during  expansion  freed  the  piston 
suddenly  so  that  it  made  a  number  of  quick  oscilla- 
tions, during  which  action  the  pencil  moved  so  rap- 
idly that  it  drew  a  succession  of  dots  instead  of  a  con- 
tinuous curve;  for  the  next  revolution  the  pencil  rose 
during  compression  and  admission  until  the  piston 


FIG.  70. 

stuck  again  and  was  freed  suddenly,  making  a  char- 
acteristic square  step  in  the  diagram,  after  which  the 
pencil  followed  the  normal  diagram;  the  succeeding 
revolution  shows  only  a  little  sticking  after  admission, 
and  the  fourth  revolution  gives  the  normal  diagram. 
Whenever  an  indicator  gives  a  straight  line  and  a 
square  step  it  is  well  to  look  for  friction;  for  example, 


THE   STEAM-ENGINE  INDICATOR.  121 

Fig.  70,  from  a  yacht-engine  shows  piston-friction 
very  plainly. 

When  diagrams  are  taken  at  intervals  during  a 
long  test,  the  indicators  must  be  cleaned  occasionally 
to  avoid  friction.  When  diagrams  are  taken  in  rapid 
succession,  as  during  speed  tests  of  steamships,  it  is 
advisable  to  keep  indicators  in  reserve  ready  for  im- 
mediate use  when  there  is  evidence  of  friction  in  the 
indicators  attached  to  the  engine. 

Valve  Setting. — The  valves  of  an  engine  should 
always  be  set  mechanically  by  measurement;  after  the 
valves  are  set  it  is  well  to  take  diagrams  to  detect 
errors  or  defects,  if  there  are  any.  The  indicator  dia- 
gram may  also  call  attention  to  improper  restrictions 
of  steam  pipes  or  passages,  or  to  obstructions  in  them. 

Figs.  71  and  72  were  taken  from  a  slide-valve  en- 


FIG.  71. 

gine  which  was  set  to  give  equal  cut-off;  in  such  case 
the  lead  at  the  head  end  is  likely  to  be  too  small  and 
that  at  the  crank  end  too  large.  Fig.  71  from  the 
head  end  of  the  cylinder  has  an  admission-line  that 
leans  slightly  to  the  right,  wrhile  the  admission-line  of 
Fig.  72  leans  toward  the  left.  Fig.  71  shows  also  a 
peculiarity  of  a  slide-valve  which  gives  a  large  com- 


122  THE   STEAM-ENGINE   INDICATOR. 

pression;  the  compression-line  at  first  rises  rapidly, 
then  its  rise  is  checked,  and  finally  it  falls  so  as  to 


FIG.  72. 

form  a  hook;  this  action  is  to  be  attributed  to  leakage 
under  the  valve  to  the  exhaust-space  or  past  the 
piston. 

Fig.  73,  taken  from  the  same  engine,  shows  the 
effect   of  slipping   the   eccentric;   the   cut-off  is   de- 


FIG.  73. 

layed,  the  release  is  late,  and  the  exhaust  is  defective, 
especially  at  the  beginning  of  the  return-stroke;  the 
compression  has  almost  disappeared,  and  admission 
does  not  occur  till  after  the  piston  has  started  on  the 
forward  stroke.  Fig.  74  was  taken  after  the  eccentric 
had  been  given  an  excessive  angular  advance,  which 
gave  the  engine  an  excessive  lead,  a  short  cut-off,  and 
an  early  release.  A  notable  feature  is  the  oscillation 


THE  STEAM-ENGINE   INDICATOR.  12$ 

at  admission,  which  is  here  spread  out  instead  of  being 
confined  as  in  Fig*.  71. 

Compound  Engines. — With  the  use  of  high-pres- 
sure steam  it  has  become  the  practice  to  use  the 
steam  in  two  or  more  cylinders  successively,  as  by 
that  means  the  ill  effects  of  cylinder  condensation  can 
be  ameliorated.  A  compound  engine  has  two  cylin- 
ders, a  small  cylinder  which  receives  steam  from  the 


FIG.  74- 

boiler,  and  a  large  cylinder  which  takes  the  steam 
from  the  small  cylinder  and  delivers  it  to  the  con- 
denser. A  triple  engine  has  three  successive  cylin- 
ders, and  a  quadruple  engine  has  four  successive 
cylinders.  Sometimes  the  large  or  low-pressure  cylin- 
der is  divided,  or  two  cylinders  are  used  together  in 
place  of  the  low-pressure  cylinder.  Many  marine  en- 
gines at  the  present  time  have  four  cylinders,  a  high- 
pressure  cylinder,  an  intermediate  cylinder,  and  two 
low-pressure  cylinders. 

If  a  compound  or  multiple-expansion  engine  has  a 
large  receiver  between  the  successive  cylinders,  into 


124 


THE   STEAM-ENGINE   INDICATOR. 


which  the  steam  is  exhausted  by  the  smaller  cylinder 
and  from  which  steam  is  supplied  to  the  larger  cylin- 
der, then  the  diagrams  look  much  like  those  taken 
from  simple  engines;  if  there  is  but  a  small  space 
the  diagrams  may  appear  to  be  much  distorted. 

Diagrams  of  the  first  type  are  given  by  Figs.  75 


FIG.  75. 


FIG.  76. 

and  76,  taken  from  a  compound  pumping-engine  with 
cranks  at  right  angles  and  with  an  intermediate  re- 
ceiver. The  back-pressure  line  of  the  high-pressure 
diagram  rises  a  little  at  the  middle  of  the  stroke,  cor- 
responding with  the  admission  to  the  low-pressure 
cylinders.  The  low-pressure  diagram  shows  a  distinct 
falling-off  in  the  admission-line  at  about  one  fifth 
stroke,  due  to  the  closing  of  the  exhaust-port  of  the 


THE   STEAM-ENGINE  INDICATOR. 


125 


high-pressure  cylinder;  from  that  point  to  the  cut-off 
at  about  3/10  stroke  the  low-pressure  cylinder  draws 
steam  from  the  receiver  with  falling  pressure.  With 
these  exceptions  the  diagrams  resemble  those  taken 
from  simple  engines. 

Figs.  77  and  78  give  diagrams  from  a  compound 
pumping-engine  at   Louisville,  Ky.,  which  has  the 


FIG.  77- 


FIG.  78. 

high-pressure  and  low-pressure  pistons  connected  to 
opposite  ends  of  a  short  beam,  so  that  one  rises  while 
the  other  falls.  Steam  is  transferred  from  the  upper 
end  of  the  high-pressure  cylinder  to  the  upper  end  of 
the  low-pressure  cylinder  through  a  receiver,  and  in 
the  same  way  from  the  lower  end  of  the  small  cylin- 
der to  the  same  end  of  the  large  cylinder.  Admis- 
sion to  the  low-pressure  cylinder  from  the  begin- 
ning of  the  stroke  up  to  cut-off  consists  of  a  direct 
transfer  of  steam  to  it  from  the  high-pressure  cylin- 


126 


THE  STEAM-ENGINE  INDICATOR. 


der;  the  low-pressure  piston  has  four  times  the  area 
of  the  high-pressure  piston,  so  that  the  volume  of 
the  steam  increases  during  this  transfer  and  the  pres- 
sure falls.  The  back-pressure  line  of  the  high-pres- 
sure diagram  is  affected  by  this  fall  of  pressure  until 
cut-off  occurs  on  the  low-pressure  cylinder;  after  that 
the  back-pressure  line  of  the  high-pressure  diagram 


FIG.  79. 

rises.    The  relation  of  the  diagrams  during  the  action 
just  described  is  made  clearer  by  redrawing  the  dia- 


THE   STEAM-ENGINE   INDICATOR. 


127 


grams  one  above  the  other  and  with  the  same  scale 
of  pressure  as  in  Fig.  79. 

Diagrams  from  the  triple-expansion  engine  at  the 
Massachusetts  Institute  of  Technology  are  shown  by 
Figs  80,  81,  and  82;  this  engine  has  three  horizontal 


FIG.  80. 


FIG.  81, 


FIG.  82. 

cylinders  with  diameters  9,  16,  and  24  inches,  and  a 
stroke  of  30  inches;  all  the  cylinders  are  jacketed  with 
steam  on  the  heads  and  barrels.  The  back-pressure 
lines  of  the  high-pressure  and  intermediate  diagrams 
show  some  fluctuation  of  pressure  due  to  the  exhaust 
of  steam  to  receivers,  and  to  the  supply  of  steam  from 


128 


THE    STEAM-ENGINE   INDICATOR. 


the  receivers  to  the  intermediate  and  low-pressure  cyl- 
inders. The  steam-lines  of  the  intermediate  and  low- 
pressure  cylinders  are  also  affected  to  some  extent. 

Compound  and  triple-expansion  marine  engines 
commonly  have  no  other  receiver-spaces  between  suc- 
cessive cylinders  than  is  provided  by  steam-chests  and 
steam-pipes.  There  are  consequently  large  fluctua- 
tions of  pressure  due  to  the  irregular  way  in  which 


FIG.  83. 


FIG.  84. 


FIG.  85. 

steam  is  exhausted  into  and  drawn  from  these  spaces! 
Figs.  83,  84  and  85  give  diagrams  from  the  U.  S.  S. 
Manning;  the  back-pressure  lines  of  the  high-pressure 


THE  STEAM-ENGINE  INDICATOR.  129 

and  intermediate  diagrams,  and  the  steam-lines  of  the 
intermediate  and  low-pressure  diagrams,  show  con- 
siderable irregularity  due  to  the  causes  named. 

Combined  Diagrams. — Attempts  are  sometimes 
made  to  get  a  diagram  which  will  show  the  combined 
action  of  the  several  cylinders  of  a  compound  or  mul- 
tiple-expansion engine.  The  simplest  method  of  mak- 


FIG.  86. 


ing  a  combined  diagram  is  shown  by  Fig.  86,  where 
the  diagrams  from  a  triple  engine  (Figs.  83,  84,  and 
85)  are  redrawn,  using  the  same  vertical  scale  and 
making  the  horizontal  scale  proportional  to  the  pis- 


1 30  THE   STEAM-ENGINE   INDICATOR. 

ton-displacements  of  the  several  cylinders.  The  dia- 
grams are  then  referred  to  axes  of  zero  volume  and 
zero  pressure  as  explained  on  page  114,  Fig.  64;  each 
diagram  being  drawn  separately  and  with  its  own 
clearance.  The  diagram  is  completed  by  drawing  a 
hyperbola  through  the  cut-off  of  the  high-pressure 
cylinder. 

It  does  not  appear  that  any  combined  diagram  is 
satisfactory,  or  that  any  important  lesson  can  be 
learned  from  such  a  diagram.  This  may  be  attributed 
to  the  clearances  of  the  cylinders,  and  to  the  restric- 
tion of  the  capacity  of  the  receiver-spaces  between 
the  cylinders.  If  one  could  have  an  engine  without 
clearances,  with  very  large  receiver-spaces,  and  with 
cylinders  made  of  non-conducting  material,  then  a 
logical  and  useful  combined  diagram  could  be  drawn; 
the  discussion  of  such  an  engine  and  the  drawing  of 
the  diagram  is  properly  considered  in  a  treatise  on 
thermodynamics.  It  may  be  noted  that  the  discussion 
includes  that  of  an  engine  with  concordant  pistons, 
like  the  Louisville  engine,  and  without  receiver- 
spaces.  In  order  that  a  logical  combined  diagram 
may  be  drawn  with  clearances  it  is  essential  that  the 
clearances  and  the  compressions  shall  be  chosen  so 
that  the  weight  of  steam  caught  at  compression  shall 
be  the  same  for  all  cylinders;  this  is  not  done  in  prac- 
tice, and  there  seems  to  be  no  good  reason  for  doing 
so.  Again,  the  transfers  of  steam  from  a  cylinder  to 
a  receiver  and  from  that  receiver  to  the  succeeding 


THE  STEAM-ENGINE   INDICATOR.  13 l 

cylinder,  as,  for  example,  that  shown  by  Figs.  77  and 
78  for  the  Louisville  engine,  have  certain  relations 
which  are  not  shown  at  all  in  the  combined  diagram, 
or  else  they  are  misrepresented.  Finally  the  hyper- 
bola has  a  doubtful  place  on  any  steam-engine  dia- 
gram, and  can  have  no  relation  to  more  than  one  indi- 
vidual diagram  of  any  combined  diagram.  Attempts 
have  been  made  to  meet  the  several  objections  that 
have  been  mentioned  to  the  method  here  given  for 
combining  diagrams  from  compound  engines  which 
have  on  the  whole  added  to  the  complexity  of  the 
diagram  without  making  it  more  logical  or  more 
useful.  Other  curves  than  the  hyperbolae  have  some- 
times been  drawn  on  combined  diagrams,  such  as  the 
adiabatic  line  which  would  be  drawn  by  an  indicator 
for  expansion  in  a  non-conducting  cylinder;  such 
curves,  again,  increase  the  labor  of  drawing  the  dia- 
gram without  adding  to  its  usefulness. 

Pump  Diagrams. — Indicator  diagrams  are  taken 
from  the  pump  cylinders  or  pump  chambers  of  pump- 
ing-engines  to  reveal  the  losses  of  pressure  on  the 
way  to  and  from  the  pump,  to  determine  the  power  ex- 
pended in  the  pump,  and  to  investigate  the  action  of 
the  pump  valves.  A  discussion  of  the  actions  of 
pumps  and  their  valves  is  too  large  a  subject  to  take 
up  here.  It  will  suffice  to  give  a  few  examp^s.  Fig. 
87  gives  a  diagram  taken  from  the  engine  at  Louis- 
ville, and  Fig.  88  a  diagram  from  the  engine  at  Ches*> 
nut  Hill;  the  former  makes  18.5  revolutions  per  min- 


132 


THE   STEAM-ENGINE  INDICATOR. 


ute,  and  the  second  makes  50.5  revolutions  per  min- 
ute.    It  is  but  proper  to  call  attention  to  the  fact  that 


FIG.  87. 


FIG.  88. 

while  the  oscillations  in  a  pump  diagram  are  due  to 
shocks  and  sudden  changes  of  pressure,  they  belong 


FIG.  89. 


FIG.  90. 

rather  to  the  indicator  than  to  the  pump,  as  is  also 
the  case  with  oscillations  in  a  steam-engine  diagram. 
Direct-acting  Pumping-engine. — Figs.  89  and  90  give 


THE   STEAM-ENGINE  INDICATOR.  133 

diagrams  from  the  steam-cylinders  and  the  pump-cyl- 
inder of  a  compound  duplex  direct-acting  pumping- 
engine.  The  diagrams  from  the  high-pressure  cylinder 
and  the  low-pressure  cylinder  are  superimposed  in 
their  proper  relation.  Steam  is  supplied  to  the  high- 
pressure  cylinders  through  the  whole  forward  stroke, 
and  is  transferred  through  a  receiver  to  the  low- 
pressure  cylinder  through  the  whole  return- 
stroke.  This  engine  has  no  fly-wheel  and  cannot 
have  a  cut-off  for  either  cylinder;  moreover,  there 
must  be  a  large  receiver-space  so  that  the  fall 
of  pressure  during  the  transfer  of  steam  from  the 
high-pressure  to  the  low-pressure  cylinder  shall  be 
moderate.  The  high-pressure  diagram  shows  a  rise 
of  pressure  at  about  quarter-stroke  due  to  the  pause 
which  the  other  engine  makes  at  the  end  of  a  stroke 
before  beginning  another.  Each  low-pressure  cylin- 
der of  the  engine  has  separate  steam  and  exhaust  pas- 
sages, the  latter  being  inside.  When  the  piston  nears 
the  end  of  its  stroke  it  overruns  and  closes  the  ex- 
haust-passage, and  thus  produces  a  compression  to 
stop  the  engine  at  the  end  of  the  stroke.  The  exact 
compression  required  is  attained  by  providing  a  by- 
pass valve  through  which  the  steam  caught  at  com- 
pression can  leak  out;  if  this  valve  is  closed  the  en- 
gine makes  a  short  stroke;  the  valve  can  then  be 
opened  to  such  an  extent  that  the  piston  shall  nearly 
but  not  quite  strike  the  cylinder  head. 

The  pump  diagram  shows  a  ragged  line  at  the  left 


134  THE  STEAM-ENGINE  INDICATOR. 

end  caused  by  the  superposition  of  oscillations  of  the 
indicator-pencil,  due  to  the  sudden  rise  of  pressure  in 
the  pump  chamber  when  the  pump  is  reversed;  there 
are  also  oscillations  near  the  right  end  which  are 
transmitted  from  the  other  pump  when  that  engine 
reverses. 

Air-compressor. — A  diagram  from  an  air-com- 
pressor is  represented  by  Fig.  91;  at  the  beginning  of 
the  stroke  the  air  in  the  clearance-space  is  expanded 
down  to  or  a  little  below  the  pressure  of  the  atmos- 

.d 


FIG.  91. 

phere  as  represented  by  ab]  the  pressure  rises  to  that 
of  the  atmosphere  as  soon  as  the  admission-valve 
opens  and  the  cylinder  is  filled  as  represented  by  be; 
the  compression  is  represented  by  cd;  and  from  d  to  a 
the  air  is  forced  into  a  reservoir,  the  variations  of 
pressure  being  due  to  the  action  of  the  delivery- 
valves.  This  diagram  was  taken  from  the  larger  cyl- 
inder of  a  compound  or  two-stage  compressor,  which 
compresses  air  to  about  37  pounds  above  the  atmos- 
phere and  delivers  it  to  a  tubular  intercooler.  Cold 
water  circulated  through  the  pipes  of  the  intercooler 
cools  the  air  to  the  temperature  of  the  atmosphere, 
with  a  notable  reduction  in  volume.  The  cooled  air  is 


THE   STEAM-ENGINE  INDICATOR. 


135 


drawn  in  by  a  smaller  cylinder,  where  it  is  further 
compressed  to  about  95  pounds  above  the  atmosphere. 
Fig.  92  shows  a  combined  diagram  of  the  diagrams 
from  both  the  cylinders  of  this  compound  compres- 
sor, drawn  with  the  same  scales  of  pressure  and  vol- 
ume as  explained  for  steam-engines  on  page  129;  the 


objections  urged  against  combined  diagrams  at  that 
place  apply  equally  here. 

On  Fig.  92  are  drawn  two  theoretical  curves  for 
air,  the  adiabatic  curve,  which  represents  compression 
in  a  perfectly  non-conducting  cylinder,  and  the  iso- 
thermal line,  which  represents  compression  at  a  con- 
stant temperature;  the  isothermal  line  is  a  rectangular 
hyperbola  for  which  the  construction  is  given  on  page 
114.  The  construction  of  adiabatic  and  isothermal 


136 


THE   STEAM-ENGINE  INDICATOR. 


curves  for  air  has  a  real  significance  because  there  is  no 
question  of  the  composition  of  the  fluid  in  the  cylin- 
der; the  case  is  quite  different  from  the  drawing  of  a 
hyperbola  on  a  steam-engine  diagram.  It  is  custom- 
ary to  cool  the  cylinder  of  a  compressor  by  injecting 
water  into  the  cylinder  or  by  circulating  water 
through  a  water-jacket;  the  effect  of  the  water  is 
mainly  to  keep  the  cylinder  cool,  for  the  air  is  cooled 
but  little  at  ordinary  pressures.  Three-  or  four-stage 
compressors,  which  deliver  air  at  1000  to  2000  pounds 
to  the  square  inch,  show  an  appreciate  cooling  of  the 
air  at  high  pressures  in  the  small  cylinders.  Fig.  92 
shows  that,  there  is  but  little  cooling  of  the  air  in  the 
large  cylinder,  for  the  compression-line  falls  only  a 
little  below  the  adiabatic  line  along  which  it  would  lie 
were  there  absolutely  no  cooling.  The  isothermal  line 


10 


passes  through  the  beginning  of  each  diagram,  which 
shows  that  the  intercooler  reduces  the  temperature  cf 
the  air  to  that  of  the  atmosphere.  To  avoid  confusion, 
the  adiabatic  line  for  the  small  cylinder  is  omitted. 


THE   STEAM-ENGINE  INDICATOR.  137 

The  overlapping  of  the  diagrams  exhibits  the  fact  that 
some  pressure  is  required  to  force  the  air  through  the 
intercooler  into  the  small  cylinder. 

The  isothermal  line  can  be  drawn  as  explained  on 
page  114,  Fig.  64,  and  shown  by  Fig.  93,  by  di- 
viding the  space  from  c  to  the  axis  (including 
the  clearance)  into  a  convenient  number  of  equal 
parts,  ten  for  example.  The  dividing  points  may 
be  numbered  o.i,  0.2,  0.3,  0.4,  0.5,  0.6,  0.7,  0.8, 
and  0.9;  on  lines  drawn  through  these  points  we 
may  lay  off  pressures  obtained  by  dividing  the 
pressure  at  c  by  the  decimals  at  the  points  of  division; 
or  the  required  pressures  can  be  obtained  by  multi- 
plying the  pressure  at  c  by  the  factors  given  in  the  sec- 
ond line  of  the  following  table: 

TABLE   FOR   DRAWING  ISOTHERMALS  AND  ADIABATICS   OF  AIR. 

Points 0.2       0.3         0.4         0.5  0.6         0.7         0.8        0.9 

Isothermal..    5           3.33       2.5         2.0  1.67       1.43       1.25       i.n 

Adiabatic 9.6       5.43       3.62       2.65  2.05       1.65       1.37      1.16 

The  points  on  the  adiabatic  line  may  be  found  by 
laying  off  from  the  points  of  division  pressures  found 
by  multiplying  the  pressure  at  c  by  the  factors  given 
on  the  third  line  of  the  table;  the  method  of  calcu- 
lating these  factors  can  be  deduced  from  the  theoreti- 
cal investigation  of  air  in  any  treatise  on  thermody- 
namics. 

Air-pump. — An  air-pump  has  for  its  main  duty  the 
removal  of  air  from  the  condenser;  this  air  is  brought 
in  by  the  condensing  water  of  a  jet  condenser,  or  else 


138 


THE   STEAM  ENGINE  INDICATOR. 


it  leaks  in  around  the  piston-rod  of  the  engine  or  else- 
where; a  surface  condenser  is  subject  to  accumulation 
of  air  mainly,  if  not  entirely,  by  such  leakage.  A  com- 
parison of  Fig.  94,  taken  from  an  air-pump,  with  Fig. 
91,  from  an  air-compressor,  will  show  the  essential 
similarity  between  the  two  machines. 

Air  and  vapor  in  the  clearance  of  the  air-pump  are 
expanded  from  a  to  b  till  the  pressure  is  somewhat  less 


FIG.  94. 

than  the  absolute  pressure  in  the  condenser;  during 
this  operation  there  may  be  some  vaporization  of 
water  in  the  air-pump.  The  pump  draws  air  and  wa- 


FIG.  95. 

ter  from  the  condenser  from  b  to  c;  from  c  to  d  the  air 
and  any  vapor  in  the  pump  are  compressed  up  to  the 
pressure  of  the  atmosphere;  from  d  to  a  air  and  water 


THE   STEAM-ENGINE  INDICATOR.  139 

are  forced  out  through  the  delivery-valves  of  the  air- 
pump. 

Fig.  95  gives  the  diagram  from  the  steam-cylinder 
which  drives  the  air-pump  from  which  Fig.  94  was 
taken.  This  air-pump  is  arranged  like  a  direct-acting 
steam-pump  with  the  steam-piston  and  pump  piston 
on  one  rod  and  without  a  fly-wheel.  Such  an  arrange- 
ment for  a  water-pump  is  good  mechanically,  because 
the  constant  resistance  of  the  pressure  of  the  water 
requires  a  constant  pressure  in  the  steam-cylinder  for 
smooth  running;  but  the  air-pump  diagram  shows  no 
resistance  at  the  beginning  of  the  stroke;  indeed  the 
air  in  the  clearance  urges  the  pump  piston  forward  till 
the  admission-valves  open  to  supply  air  to  the  filling 
end  of  the  pump  cylinder.  After  the  pump  has  made 
half  to  three-quarters  of  its  stroke  the  pressure  of  the 
air  on  the  delivering  end  of  the  air-pump  is  raised  by 
compression  so  that  it  offers  a  large  resistance;  the 
effect  of  this  action  is  that  the  pump  and  steam  pis- 
tons jump  quickly  half  or  more  of  their  stroke,  then 
they  are  checked,  and  complete  the  stroke  slowly. 
To  avoid  too  great  irregularity  of  action  the  steam- 
passages  are  restricted  so  that  the  steam  is  throttled 
from  e  to  f  while  the  pistons  jump  forward;  the  steam- 
pressure  rises  from  f  to  g,  and  the  stroke  is  completed 
under  nearly  full  steam-pressure  from  g  to  h.  During 
the  return-stroke  the  back-pressure  line  is  raised  dur- 
ing the  sudden  motion  of  the  piston  for  half  or  more 
of  the  stroke,  but  when  the  pistons  slow  up  and  com- 


140  THE   STEAM-ENGINE   INDICATOR. 

plete  the  stroke  quietly  the  back-pressure  line  drops 
as  shown  by  klm.  In  conclusion  we  see  that  the 
steam-cylinder  is  finally  filled  at  full  steam-pressure, 
and  that  it  exhausts  its  steam  completely,  but  the 
effective  area  is  much  reduced;  from  which  we  recog- 
nize that  the  direct-acting  air-pump  must  use  a  large 
amount  of  steam  per  horse-power  per  hour. 

Gas-engines. — The  explosive  or  internal-combus- 
tion gas-engine  is  a  single-acting  engine  which  makes 
two  revolutions,  and  four  strokes  of  its  piston,  for 
each  working  impulse.  Fig.  96  is  a  diagram  from  a 


FIG.  96. 

35-horse-power  gas-engine  at  the  Massachusetts  In- 
stitute of  Technology.  The  first  or  filling  stroke 
draws  in  an  explosive  mixture  of  gas  and  air  as  repre- 
sented by  ab;  the  second  stroke  compresses  the  charge 
from  b  to  c,  giving  a  pressure  of  60  pounds  at  c;  at  c 
the  charge  is  ignited  by  an  electric  spark,  and  the 
pressure  rises  to  310  pounds  at  d;  work  is  done  during 
the  expanding  or  working  stroke,  represented  by  de\ 
at  e  release  occurs,  and  the  contents  of  the  cylinder  are 
exhausted  during  the  fourth  stroke,  bringing  the  dia- 
gram to  its  close  at  a. 


THE  STEAM-ENGINE  INDICATOR.  141 

Gasoline-engines  are  explosion  engines  which  are 
charged  with  a  mixture  of  air  and  vapor  of  gasoline 
which  is  made  as  it  is  used.  Oil-engines  use  a  safe  oil 
like  kerosene;  as  kerosene  will  not  vaporize  com- 
pletely like  gasoline,  special  arrangements  are  re- 
quired for  spraying  it  or  otherwise  mixing  it  with  air. 
Deisel  Motor. — This  engine  is  an  internal-combustion 
engine  which  makes  four  strokes  for  each  impulse,  as 
does  the  gas-engine.  During  the  filling  stroke  only 
atmospheric  air  is  drawn  in,  and  this  air  is  compressed 
during  the  second  stroke  to  500  pounds  pressure  and  is 
heated  to  1000°  F.  Oil  of  any  character,  including 
heavy  petroleum  refuse,  may  be  injected  into  the  cyl- 


FIG.  97. 

inder  after  the  compression  is  completed,  and  will  burn 
immediately  in  the  strongly  heated  air;  after  the  oil 
has  been  injected  the  engine  makes  its  expansion  or 
working  stroke.  Fig.  97  shows  the  similarity  to  the 
ordinary  gas-engine. 

Ammonia  Refrigerating-machine. — An   intense   de- 


142 


THE  STEAM-ENGINE  INDICATOR. 


gree  of  cold  can  be  attained  by  vaporizing  a  volatile 
liquid  like  ammonia,  which  boils  at  —  27°  F.,  under 
the  pressure  of  the  atmosphere.  In  order  to  use  the 
vapor  again  it  must  be  compressed,  and  liquefied  at 
or  about  the  temperature  of  the  atmosphere,  by  the  aid 
of  a  stream  of  cooling  water.  Fig.  98  shows  a  dia- 
gram from  the  compression-cylinder  of  an  ammonia 
refrigerating-machine.  From  a  to  b  the  pressure  falls 


FIG.  98. 

until  the  inlet-valves  open,  and  then  the  compression- 
cylinder  fills  with  vapor  of  ammonia,  which  comes 
from  the  vaporizing  coils  of  pipes,  where  a  low  tem- 
perature is  produced.  At  the  end  of  the  filling  stroke 
be  the  compression  begins,  and  is  carried  at  d  to  the 
pressure  in  the  condenser;  da  represents  the  forcing 
of  the  vapor  through  the  delivery-valves  into  the  con- 
denser; the  irregularity  of  the  line  da  is  due  to  the 
fluttering  of  the  valves.  The  condenser  is  made  of 
coils  of  pipe  cooled  by  water,  which  may  flow 
over  the  pipes  or  may  circulate  among  them,  ac- 


THE   STEAM-ENGINE  INDICATOR.  143 

cording  to  the  arrangement  of  the  condenser. 
The  vapor  drawn  into  the  compressor  cylinder  is 
usually  dry,  that  is,  it  contains  no  liquid  am- 
monia. If  that  is  so,  the  compression-curve  agrees 
nearly  with  the  adiabatic  line  for  superheated  or  gas- 
eous ammonia.  This  adiabatic  line  may  be  constructed 
in  the  same  way  as  the  adiabatic  line  for  a  perfect  gas, 
as  shown  by  Fig.  93,  page  136,  except  that  the  multi- 
pliers must  be  taken  from  the  following  table: 

TABLE   FOR  ADIABATIC   LINE   FOR  AMMONIA. 

Points 0.2         0.3         0.4        0.5         0.6         0.7         0.8        0.9 

Multipliers.  8.55       4.98       3.39       2.52       1.98       1.61       1.35      1.15 

If  the  engineer  in  charge  of  an  ammonia  compres- 
sor has  found,  by  drawing  adiabatic  lines  on  diagrams 
taken  when  the  compressor  is  in  good  condition,  the 
proper  relation  between  the  compression-line  and  the 
corresponding  adiabatic  line,  then  he  may  infer  from 
the  application  of  that  line  to  a  given  diagram  what 
the  condition  of  the  compressor  is;  he  may  be  able 
thus  to  locate  leaks  in  valves  or  past  the  piston. 


APPENDIX. 

TABLES:— AREAS  OF  CIRCLES— PROPERTIES  OF 
SATURATED  STEAM— HEAT  OF  THE  LfQUID 
—LOGARITHMS. 


APPENDIX. 
TABLE  I. 

AREAS   OF  CIRCLES. 


147 


Diam. 

Area. 

Diam. 

Area. 

Diam. 

Area. 

Diam. 

Area. 

Diam. 

Area. 

.1963 

I3 

132-7 

28 

615.8 

46 

1662 

76 

4537 

a 

.2485 

13* 

137-9 

28} 

^26.8 

46* 

1698 

4596 

.3068 

^3* 

28* 

637-9 

47 

1735 

77 

4657 

i 

•  3712 

13* 

148.5 

28} 

649.2 

47* 

1772 

77* 

47>7 

.4418 

J53-9 

29 

660.5 

48 

1810 

78 

4778 

i 

.5185 
.6013 

14* 
M* 

159-5 
165.1 

29* 
29* 

672.0 
683.5 

48* 
49 

1847 
1886 

78* 
79 

4840 
4902 

11 

.6903 

14* 

170.9 

29* 

605.1 

49* 

1924 

79* 

4963 

.7854 

'5 

176.7 

30 

706.9 

50 

1964 

80 

5027 

I* 

.9940 

15* 

182.6 

30* 

718.7 

50* 

2003 

8oj 

5090 

1} 

1.227 

'5* 

188.7 

30* 

730.6 

51 

2043 

81 

5153 

»t 

1.485 

i5* 

194.8 

3o* 

742.6 

5i* 

2083 

81} 

5217 

i* 

1.767 

16 

20  1  .  i 

31 

754.8 

52 

2124 

82 

5281 

2.074 

16* 

207.4 

3i* 

767.0 

2165 

82* 

5346 

i! 

2.405 
2.761 

16* 
16* 

213.8 
220.4 

3'* 

779-3 
791-7 

i! 

2206 

2248 

83 
83* 

54" 
5476 

2 

3-142 

17 

227.0 

32 

804.2 

54 

2290 

84 

5542 

i 

4-909 

I7i 
17* 

233-7 
240.5 

32* 

32* 

816  9 
829.6 

54* 

55 

2333 
2375 

84* 
85 

5608 
5675 

5-940 

17* 

247-5 

32* 

842.4 

55* 

2419 

85* 

5742 

3 

7.069 

18 

254-5 

31 

855.3 

56 

2*63 

86 

5809 

3* 

8.296 

18* 

261.6 

33* 

868.3 

56* 

2507 

86* 

5877 

II 

9.621 
11.04 

18* 

18} 

268.8 
276.  i 

33t 
33* 

881.4 
894.6 

2552 
2597 

87 

87* 

5945 
6013 

4 

"•57 

19 

283-5 

34 

907.9 

58 

2642 

88 

6082 

4* 

14.19 

19* 

291.0 

34* 

921.3 

58* 

2688 

88* 

6151 

4* 

15.90 

19* 

298.6 

34* 

934.8 

59 

2734 

89 

6221 

4* 

17.72 

19* 

306.4 

34* 

948.4 

59* 

2781 

89* 

6291 

5 

19.64 

20 

314.2 

35 

962.1 

60 

2827 

90 

6362 

5* 

21.65 

20* 

322.1 

35* 

975.9 

60* 

2875 

90* 

6432 

5* 

23.75 

20* 

330.1 

35* 

989.8 

61 

2922 

91 

6504 

5* 

25.97 

20} 

338.2 

35* 

1004 

61* 

2971 

94 

6576 

6 

28.27 

21 

346.4 

36 

1018 

62 

3019 

92 

6648 

6* 

30.68 

21} 

354-7 

36* 

1032 

62* 

3068 

92* 

6720 

33-i8 

21* 

363.1 

36* 

1046 

63 

31*7 

93 

6793 

6} 

35.78 

21} 

371-5 

36* 

1061 

63* 

3l67 

93* 

6866 

7 

38.48 

22 

380.1 

37 

1075 

64 

3217 

94 

6940 

7* 
7* 

41.28 
44-18 

a 

388.8 
397-6 

37* 
37* 

1090 
1105 

64* 
65 

3268 
33'8 

94* 
95  1 

7014 
7088 

7* 
8 

47.17 
50.27 

22} 
23 

406.5 
4I5.5 

37* 
38 

1  120 

"34 

65* 
66 

3370 
3421 

7163 
7238 

8* 

53-46 

23* 

424.6 

38* 

1149 

66* 

3474 

96* 

73M 

8* 

56.75 

23* 

433-7 

1164 

67 

97 

7390 

8* 

60.  i 

23* 

443-0 

38* 

"79 

67* 

3578 

97* 

7466 

9 

63.62 

24 

452.4 

39 

"95 

68 

3632 

98 

7543 

9* 

67.20 

24* 

461.9 

39* 

1210 

68  i 

3685 

98* 

7620 

9* 

70.88 

24* 

471.4 

39* 

1225 

69 

3739 

99 

7697 

9* 

74-66 

24} 

481.1 

39* 

1241 

69* 

3794 

99* 

7776 

10 

78.54 

25 

490-9 

40 

1257 

70 

3848 

100 

7854 

10} 

82.52 

25* 

500.7 

40* 

1288 

70* 

39°4 

101 

Son 

10* 

86.59 

25* 

510.7 

4* 

1320 

7' 

3959 

102 

8171     - 

10} 

90.76 

25* 

520.8 

4'* 

1352 

4015 

lO^ 

8332 

II 

95-03 

26 

530-9 

42 

1385 

72 

4072 

104 

8495 

"* 

99-50 

26} 

541.2 

42* 

1418 

72* 

4128 

105 

8659 

11* 

103.9 

26* 

551-5 

43 

H52 

73 

4185 

106 

8825 

108.4 

26} 

562.0 

43* 

1487 

73* 

4243 

107 

8992 

12 

"3-1 

27 

572.6 

44 

1521 

74 

4301 

108 

9161 

12} 

117.9 

27* 

583.2 

44* 

T555 

74* 

4359 

109 

9331 

12* 
12} 

122.7 
127.7 

27* 
27* 

& 

'590 
1626 

4418 
4477 

110 

in 

9503 
9677 

148 


APPENDIX. 
TABLE  II. 

PROPERTIES  OF  SATURATED  STEAM. 


Volume 

Weight 

Pressure 
Pounds 
per 
Square 
Inch. 

Tempera- 
ture 
Degrees 
Fahren- 
heit. 

Heat 
of  the 
Liquid. 

Total 
Heat. 

Heat 
of 
Vaporiza- 
tion. 

in 
Cubic 
Feet 
of 
One 

in 
Pounds 
of 
One 
Cubic 

Pressure 
Pounds 
per 
Square 
Inch. 

Pound. 

Foot. 

' 

t 

g 

h 

r 

V 

d 

* 

i 

T02 

70.0 

1113.1 

1043.0 

334-6 

0.00299 

I 

2 

126.3 

94.4 

1120.5 

1026.1 

173-6 

0.00576 

2 

3 

141.6 

109.8 

1125.1 

1015.3 

118.4 

0.00844 

3 

4 

igg.I 

121.4 

1128.6 

1007.3 

90.31 

0.01107 

4 

5 

162.3 

*30-7 

1131  .5 

1000.8 

73.22 

0.01366 

5 

6 

170.1 

138.6 

"33-8 

995-2 

61.67 

0.01622 

6 

7 

176.9 

M5-4 

"35-9 

990-5 

53-37 

0.01874 

7 

8 

182.9 

H37-7 

986.2 

47.07 

0.02125 

8 

9 

t88.3 

156.9 

"39-4 

982.5 

4a-I3 

0.02374 

9 

10 

193  .3 

161  .9 

1140.9 

979.0 

38.16 

0.02621 

10 

ii 

197.78 

166.5 

"42  3 

975-8 

34-88 

0.02866 

ii 

12 

202  o 

1  70.7 

1143.6 

972.9 

32-  >4 

0.03111 

12 

13 

205.9 

174.6 

1144.7 

970.1 

29.82 

0.03355 

13 

14 

209.6 

178.3 

H45.8 

967-5 

27  -79 

o  .  03600 

14 

212.0 

180.3 

1146.6 

965-8 

26.60 

0.03760 

16 

216.3 

185.1 

1147.9 

962.8 

24-59 

0.04067 

16 

18 

222.4 

i9'-3 

1149.8 

958.5 

22.  CO 

0.04547 

18 

20 

228.0 

196  9 

"5'«  5 

954-6 

19.01 

0.05023 

20 

22 

233-1 

202.  o 

1153.0 

951.0 

18.20 

0-05495 

22 

»4 

237-8 

206.8 

"54-4 

947-6 

16.76 

0.05966 

24 

26 

24O.2 

211.  2 

1155.8 

944-6 

15.55 

0.06432 

26 

28 

246.4 

215-4 

II57-I 

94T-7 

14.49 

0.06899 

28 

30 

250.3 

219.4 

"58.3 

938.9 

13.59 

0.07360 

30 

254.0 

223.1 

"59-4 

936.3 

12.78 

0.07820 

34 

257.5 

226.7 

1160.4 

933-7 

12.07 

0.08280 

34 

36 

260.9 

230.0 

1161.5 

931  5 

H-45 

0.08736 

36 

38 

264.  t 

233-3 

1162.5 

929.2 

10.88 

0.09191 

38 

267.1 

236.4 

1163  4 

927.0 

10.37 

0.09644 

40 

4* 

27O.  I 

239-3 

1164.3 

925.0 

9.906 

0.1009 

43 

44 

272.9 

242.2 

1165.2 

923.0 

9.484 

0.1054 

46 

275-7 

245.0 

1166.0 

921.0 

9.097 

0.1099 

46 

48 

278.3 

247.6 

n66.8 

919.2 

8.740 

0.1144 

48 

5° 

280.9 

250.2 

1167.6 

9I7-4 

8.414 

0.1188 

5° 

52 

283.3 

252  7 

1168.4 

9'5-7 

8.  1  10 

0.1233 

5* 

a 

285.7 
288.1 

255-1 
257  5 

1169.  i 
1169.8 

914.0 
912.3 

7.829 
7-568 

0.1277 
0.1321 

% 

58 

290.3 

259-7 

1170.5 

910.8 

7-323 

0.1366 

58 

60 

292.5 

261.9 

1171.2 

909-3 

7.096 

0.1409 

60 

62 

294.7 

264.1 

1171.8 

6.882 

0.1453 

62 

64 

296.7 

266.2 

1172.4 

906.2 

6.680 

0.1497 

64 

66 

298.8 

268.3 

1173.0 

904.7 

6.490 

0.1541 

66 

68 

300.8 

270-3 

1173.6 

903.3 

6.314 

0.1584 

68 

70 

302.7 

272.2 

"74-3 

902.1 

6.144 

0.1628 

70 

72 

304.6 

274.1 

1174.9 

900  8 

5-984 

0.1671 

72 

306.5 

276.0 

"75-4 

899.4 

5-834 

0.1714 

74 

76 

308.3 

277-8 

1176.0 

898.2 

5.691 

0.1757 

76 

78 

310.1 

279.6 

1176.5 

896.9 

5  554 

0.1801 

78 

80 

3«.8 

281.4 

1177.0 

895.6 

5.425 

0.1843 

80 

82 

3I3.5I 

283.2 

1177.6 

894.4 

5.301 

0.1886 

82 

APPENDIX. 
TABLE  II. — Continued. 

PROPERTIES  OF  SATURATED  STEAM. 


149 


Volume 

Weight 

Pressure 
Pounds 
per 
Square 
Inch. 

Tempera- 
ture 
Degrees 
Fahren- 
heit. 

Heat 
of  the 
Liquid. 

Total 
Heat. 

Heat 
of 

Vaporiza- 
tion. 

in 
Cubic 
Feet 
of 
One 

in 
Pounds 
of 
One 
Cubic 

Pressure 
Pounds 
per 
Square 
Inch. 

Pound. 

Foot. 

P 

t 

? 

h 

T 

V 

d 

/ 

85 

316.0 

285.8 

1178.3 

892.5 

5-125 

0.1951 

85 

go 

320.0 

290.0 

1179.6 

889.6 

4  858 

0.2058 

90 

95 

323-9 

294.0 

1180.7 

886.7 

4.619 

0.2165 

95 

100 

327.6 

297.9 

1181.9 

884.0 

4-403 

0.2271 

IOO 

JOS 

33'-1 

301.6 

1182.9 

801-3 

4.206 

0.2378 

105 

no 

334-6 

305.2 

1184.0 

878.8 

4.026 

0.2484 

no 

"5 

337-9 

308.7 

1185.0 

876.3 

3-86« 

0.2589 

"5 

1  20 

34*  -1 

312.0 

i  i  86.0 

874.0 

3«7" 

o  2695 

T20 

"5 

344-1 

315-2 

1186.9 

871.7 

3-572 

0.2800 

I2S 

13° 

347-1 

318.4 

1187.8 

869.4 

3-444 

0.2904 

130 

»3S 

350-0 

321.4 

1188.7 

867  3 

3-323 

0.3009 

*35 

140 

352.9 

324.4 

1189.5 

865.1 

3.212 

o-3"3 

140 

145 

355-6 

327.2 

1190.4 

863.2 

3-J07 

0.3218 

MS 

150 

155 

3f.3 
360.9 

330   0 

332.7 

1191.2 
i  192.0 

861.2 
859-3 

3.011 

•  Qi9 

0.3321 
0.3426 

150 
*55 

160 

36V4 

335-4 

1192.8 

857-4 

-833 

0-3530 

160 

165 

365-9 

338.0 

1193.6 

855-6 

•751 

0-3635 

165 

170 

368.3 

340.5 

JI94-3 

853.8 

.676 

0-3737 

170 

175 

370.7 

343-0 

1195.0 

852.0 

603 

0.3841 

175 

1  80 

373-0 

345-4 

iig5.7 

849-3 

•535 

0-3945 

i  So 

185 

375-2 

347-8 

1196.4 

848.6 

•470 

0.4049 

185 

190 

377-4 

350-1 

1197.1 

847.0 

.408 

0-4153 

190 

*95 

379-6 

352.4 

1197.7 

845.3 

•349 

0.4257 

195 

200 

381-7 

354-6 

1,98  4 

843  8 

•294 

0-4359 

200 

205 

383.8 

356.8 

1199.0 

842.2 

.241 

0.4461 

205 

2IO 

385-9 

358.9 

1199.6 

840.7 

.190 

o.4565 

2TO 

215 

387-9 

361.0 

I2OO.2 

839.2 

.142 

0.4669 

215 

2  2O 

389.8 

363.0 

12OO.8 

837.8 

.096 

0.4772 

220 

225 

391.8 

365.t 

I20I.4 

836.3 

.051 

o  4876 

225 

230 

393-7 

367-1 

I2O2.O 

834-9 

.009 

0-4979 

230 

235 

395-6 

369-0 

1202.6 

833-6 

.968 

0.5082 

235 

240 

397-4 

37i.o 

I2O3.2 

832.2 

.928 

0.5186 

240 

245 

399-2 

372.8 

1203.7 

830.9 

.891 

0.5289 

245 

250 

401.0 

374-7 

1204.2 

829.5 

•854 

0-5393 

350 

255 

402.7 

376.5 

1204  8 

828.3 

.819 

0.5496 

2SS 

260 

4°4-5 

378.4 

1205-3 

826.9 

-785 

0.5601 

260 

265 

406.2 

380.2 

1205.8 

825.6 

•753 

0-5705 

265 

270 

407-9 

381.9 

1206.3 

824.4 

.722 

o  5809 

270 

275 

409-5 

383-6 

1206  8 

823.2 

.691 

0-1913 

280 

411.1 

385-3 

1207.3 

822.0 

.662 

0.602 

280 

285 

412.7 

387.0 

1207.8 

820.8 

-634 

0.612 

285 

290 

4U-3 

388.6 

1208.3 

819.7 

.607 

0.622 

290 

295 

4IS.9 

390.3 

1208.8 

818.5 

.580 

0.633 

295 

300 

417.4 

39T-9 

1209.3 

8,7.4 

•554 

0.644 

300 

305 

418.9 

393-5 

1209.7 

810.2 

•529 

0.654 

305 

310 

420.4 

395-0 

I2IO.2 

815.2 

•505 

0.664 

310 

3'5 

421.9 

396.6 

I2IO.6 

814.0 

.48t 

0-675 

3*5 

320 

423-4 

398.1 

I2II.I 

813.0 

•459 

0.685 

320 

325 

424.8 

399-6 

I21I.5 

811.9 

•437 

0.696 

32S 

APPENDIX. 
TABLE  III. 

HEAT   OF  THE   LIQUID. 


Temp. 
Deg.  F. 

t 

Heat  of 
Liquid. 

q 

Temp. 
Deg.  F. 
t 

Heat  of 
Liquid. 

q 

Temp. 
Deg.  F. 

t 

Heat  of 
Liquid. 

q 

Temp. 
Deg.  F. 

t 

Heat  of 
Liquid. 

q 

32 

0 

78 

46.10 

124 

92. 

170 

nS-s 

33 

1  .01 

79 

47.09 

125 

93- 

171 

139-5 

34 

2.01 

80 

48.09 

126 

94. 

72 

140.5 

35 

3-02 

81 

49.08 

127 

95- 

73 

141-5 

36 

4.03 

82 

50.08 

128 

96. 

74 

142-5 

37 

5-04 

83 

5!-07 

129 

97- 

75 

143-5 

38 

6.04 

84 

52.07 

130 

98. 

76 

T44-5 

39 

7.05 

85 

53-o6 

131 

99. 

77 

J45-5 

40 

8.06 

86 

54.06 

132 

100. 

78 

146-5 

41 

9.06 

87 

55-05 

133 

1OI  . 

79 

H7-5 

42 

10.07 

88 

56.05 

134 

102.            ! 

180 

148.5 

43 

11  .07 

89 

57-04 

135 

103. 

181 

149-5 

44 

12.  08 

90 

58.04 

136 

104. 

182 

150.6 

45 

IJ.OS 

91 

59-03 

137 

IO5. 

183 

151  .6 

46 

14.09 

92 

60.03 

138 

106. 

184 

152-6 

47 

15.09 

93 

61  .03 

139 

107. 

185 

*53-6 

48 

16.  10 

94 

62.02 

140 

108. 

186 

154.6 

49 

17.  10 

95 

63.02 

141 

109. 

187 

I55-6 

50 

18.10 

96 

64.01 

142 

1  IO. 

188 

156.6 

51 

19.11 

97 

65.01 

143 

iti. 

189 

157-6 

52 

20.11 

98 

66.01 

144 

112.  2 

190 

158.6 

53 

21.  II 

99 

67.01 

145 

I13-3 

191 

159.6 

54 

22.11 

100 

68  01 

146 

"4-3 

192 

160.6 

55 

23.11 

101 

69.01 

147 

JI5-3 

193 

161.6 

56 

24.11 

102 

70.00 

148 

116.3 

194 

162.6 

67 

25.12 

103 

71.00 

149 

"7-3 

195 

l63-7 

58 

26.12 

104 

72.0 

150 

118.3 

196 

164.7 

59 

27.12 

105 

73-o 

151 

119.3 

197 

T6s-7 

60 

28.12 

106 

74.0 

152 

120.3 

198 

166.7 

61 

29.12 

107 

75-o 

153 

121.3 

199 

167.7 

62 

30.12 

108 

76.0 

154 

122.3 

200 

168.7 

63 

31.12 

109 

77.0 

155 

123-3 

201 

169.7 

64 

32.12 

110 

78.0 

156 

124.3 

202 

170.7 

65 

33.12 

111 

79-o 

157 

125.4 

203 

171.7 

66 

34.12 

112 

80.0 

158 

126.4     i 

204 

172.7 

67 

35-12 

113 

Bx.o 

159 

127.4 

205 

T73-7 

68 

36.12 

114 

82.0 

160 

128.4 

206 

J74-7 

69 

37.12 

115 

83.0 

161 

129.4 

207 

175-8 

70 

38-11 

116 

84.0 

162 

130.4 

208 

176.8 

71 

39-" 

117 

85.0 

163 

I3I-4 

209 

177.8 

72 

40.11 

118 

86.0 

164 

132.4 

210 

178.8 

73 

41.11 

119 

87.0 

165 

I33-4 

211 

179.8 

74 

42.11 

120 

88.1 

166 

J34-4 

212 

180.8 

75 

43-11 

121 

89.1 

167 

I35-4 

76 

44.11 

122 

90.1 

168 

136.4 

77 

45-iQ 

123 

91.1 

169 

137-4 

APPENDIX. 
TABLE  IV. 

LOGARITHMS. 


8 

Proportional  Parts, 

£ 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

c3 

123 

456 

7    8    9 

10 

oooo 

0043 

0086 

0128 

0170 

0212 

0253 

0294 

0334 

0374 

4    8    12 

17    21    25 

29  33  37 

11 

0414 

°453 

0492 

053* 

0569 

0607 

0645 

0682 

0719 

0755 

4     8     ii 

15    19    23 

26  30  34 

12 

0792 

0828 

0864 

0899 

°934 

0969 

1004 

1038 

1072 

1106 

3     7     >o 

14    17    21 

24  28  31 

13 

"39 

"73 

1206 

1239 

1271 

1303 

1335 

1367 

1399 

1430 

3     6     10 

13  16  19 

23  26  29 

14 

1461 

1492 

1523 

1553 

1584 

1614 

1644 

1673 

17°3 

1732 

369 

12  15  18 

21    24    27 

15 

,761 

1790 

1818 

1847 

1875 

1903 

1931 

T959 

1987 

2014 

3     6      8 

IT     14     17 

20   22    25 

16 

2041 

2068 

2095 

2122 

2148 

2175 

2201 

2227 

2253 

2279 

3     5      8 

ii  13  16 

18  21  24 

17 

2304 

2330 

2355 

2380 

2405 

2430 

2455 

2480 

2504 

2529 

5       7 

IO    12    15 

17    20   22 

18 

2553 

2577 

2601 

2625 

2648 

2672 

2695 

27I8 

2742 

2765 

5       7 

9  12  14 

16  19  21 

19 

2788 

2810  2833 

2856 

2878  2900 

2923 

2945 

2967 

2989 

4       7 

9  "   *3 

16  18  20 

20 

3010 

3032  3054 

3075 

3096  3118 

3139 

3160 

318. 

3201 

4       6 

8  ii  13 

*5    »7    19 

21 

3222 

3243 

3263 

J3°4 

3324 

3345 

3365 

3385 

3404 

4      6 

8  10  12 

14  16  18 

2-2 

3424 

H44  3464 

3483 

3502 

3522 

3541 

356o 

3579 

3598 

4      6 

8    10    12 

M  15  17 

23 

3617 

3636 

3655 

3674 

36^2 

37" 

3729 

3747 

3766 

3784 

4      6 

7     9  ii 

13  15  17 

24 

3802 

5820 

3838 

3856 

3874 

3892 

3909 

3927 

3945 

3962 

4       5 

79" 

12  14  16 

25 

3979 

3997 

4014 

403  * 

4048  4065 

4082 

4099 

4116 

4133 

3       5 

7     9  10 

12    14    15 

26 

4150 

4166 

4183 

42OO 

4216 

4232 

4249 

4265 

4281 

4298 

3      5 

7     8  10 

II  13  15 

27 

43H 

4330  4346 

4362 

4378 

4393 

4409 

4425 

4440 

4456 

3       5 

689 

II  13  14 

28 

4472 

4487 

4502 

4518 

4533 

4548 

4564 

4579 

4594 

4609 

3       5 

689 

II    12    14 

29 

4624 

4639  4654 

4669 

4683  4698 

47*3 

4728 

4742 

4757 

3      4 

679 

10    12    13 

30 

4771 

4786  4800 

4814 

4829  4843 

4857 

4871 

4886 

4900 

3       4 

679 

IO    II    13 

31 

4914 

4928  4942 

4955 

4969  4983 

4997 

5011 

5024 

5038 

3       4 

678 

10    II     12 

32 

5051 

5065 

5079 

S092 

5IO5 

5"9 

5i32 

SHS 

5159 

5172 

3       4 

5     7     8 

9    II    12 

33 

=^85 

5198 

52" 

5224 

5237 

5250 

5263 

5276 

5289 

5302 

3       4 

568 

9  10  12 

34 

5315 

532^5340 

5353 

5366  5378 

539' 

5403 

5416 

5428 

3      4 

5     6    8 

9  10  ii 

35 

5441 

5453  5465 

5478 

5490  5502 

55'4 

5527 

5539 

555' 

4 

5     6     7 

9  10  ii 

36 

5563 

5575 

5587 

5599 

5611 

5623 

5635 

5647 

5670 

4 

5     6     7 

8  10  ii 

37 

5682 

5694 

5705 

57[7 

5729 

5740 

5752 

5763 

5775 

5786 

3 

5     6     7 

8     9  10 

38 

5798 

5809  5821 

5832 

5343 

5855 

5866 

5877 

5888 

5899 

3 

5     6     7 

8     9  10 

39 

59" 

5922  5933 

5944 

5955 

5966 

5977 

5988 

5999 

6010 

3 

457 

8    9  10 

40 

6021 

6031 

6042 

6053 

6064  6075 

6085 

6096 

6107 

6117 

3 

4    5     6 

8     9  " 

41 

6128 

6138 

6149 

6160 

6170 

6180 

6191 

6201 

6212 

6222 

3 

4     5     6 

789 

42 

6232 

6243  6253 

6263 

6274  6284 

6294 

6304 

63M 

6325 

3 

4     5     6 

7    8    9 

43 

6335 

6345 

6355 

6365 

6375 

6385 

6395 

6405 

6415 

6425 

3 

4     5     6 

789 

44 

6435 

6444 

6454 

6464 

6474  6484 

6493 

6503 

65*3 

6522 

3 

4     5     6 

7     8    9 

45 

6532 

6542 

6551 

6561 

6571 

6580 

6590 

6599  6609 

6618 

3 

4     5    6 

789 

46 

6628 

6637 

6646 

6656 

6665 

6675 

6684 

6693  6702  6712 

3 

4     5     6 

778 

47 

6721 

6730 

6739 

6749 

6758 

6767 

6776 

6785  6794 

6803 

3 

455 

6     7    8 

48 

6812 

6821 

6830 

6839 

6848  6857 

6866 

6875 

6884 

6893 

3 

445 

678 

49 

6902 

6911 

6920 

6928 

6937 

6946 

6955 

6964 

6972 

6981 

3 

445 

6    7    8 

50 

6990 

6998  7007 

7016 

7024 

7033 

7042 

7050 

7°59 

7067 

3 

345 

678 

51 

7076 

7084 

7093 

7101 

7110 

7118 

7126 

7*35 

7*43 

7'52 

3 

345 

678 

52 

7160 

7168  7177 

7185 

7193  7202 

7210 

7218 

7226 

7235 

2 

345 

6     7     7 

53 

7243 

7251 

7259 

7267 

7275 

7284 

7292 

7300 

2 

345 

667 

64 

7324 

7332  734° 

7348 

7356  7364 

7372 

7380 

7388 

7396 

2 

345 

667 

152 


APPENDIX. 
TABLE  IV '.—Continued. 

LOGARITHMS. 


8 

Proportional  Parts. 

£ 

0 

1 

2 

3 

4 

6 

6 

7 

8 

9 

rt 

123 

456 

789 

55 

7404 

7412 

7419 

7427 

7435 

7443 

745' 

7459  7466 

7474 

345 

5     6     7 

56  (7482 

749° 

7497 

7505 

75'3 

7520  7528 

7536  7543 

755i 

345 

5     6     7 

67   |7559 

75^6 

7574 

7582 

76^7 

7589 

7597  7604 

7612  7619 

7627 

3     4     5 

5     6     7 

69    77°9 

7716 

7^49 

7723 

7°57 
773' 

7738 

7745 

/  v/  V 

7752 

7760  7767 

7774 

344 

5     6     7 

60 

7782 

7789 

7796 

7803 

7810 

781817821; 

7832  7839 

7846 

344 

566 

61    7853 

7860 

7868 

7875 

7882 

78897896 

7903  7910 

7917 

344 

5     6     6 

62  (7924 

7931 

7938  7945 

7952 

7959:7966 

7973  798o 

7987 

334 

566 

63   [7993 

8000 

8007 

8014 

8021 

8028,  803  s 

8041  8048 

8055 

334 

5     5     6 

64    8062 

8069 

8075 

8082 

8089 

8096^102 

8109  8116 

8.22 

334 

5     5    6 

65    8120 

8176 

8142 

8l4Q 

3i  6 

8162  816 

8176  8182 

8189 

66    Si.js 

J  I  JU 
?2O2 

8209 

O14v 
8215 

8222 

3228  823; 

8241  8248 

8254 

334 

5     5     6 

67    826! 
68    832^ 

8267)8274 
3331    8338 

8280 
8344 

8287 
8151 

8293  8209 
8357  8363 

8306  8312 
8370  8376 

8319 
8382 

334 
334 

5     5     6 
5     6 

69    8388 

3395 

8401 

8407 

3420  ,8426 

8432  8439 

8445 

234 

5     6 

70    8451 

3457 

8463 

8470 

8476 

8482 

8488 

8494^8500 

85of 

234 

5     6 

71  '8513 

8519 

8525 

8531 

8537 

8543 

8549 

8555856. 

8567 

234 

5     5 

72    8573 

3579 

8585 

8591 

8597 

8603 

8600 

8615  8621 

8627 

2     3     4 

5     5 

73  ,8633 
74    8692 

lell 

8645  8651 
8704  8710 

8657 
8716 

8663 
8722 

8660 
8727 

8675!868i 
8733^739 

8686 
8745 

75    8751 

8756 

8762 

8768 

8774 

8779 

8785 

8701  8797 

8802 



233 

5     5 

76  [8808 

88i4 

8820  8825 

8837 

8842 

8848  8854 

8859 

2     3     3 

5     5 

77    8865 

887i 

88768882 

S837 

8893 

8899 

8904  8910 

8915 

2     3     3 

4     5 

78    8921 

8927 

89328938 

8943 

8949 

8954 

8960  8965 

8971 

233 

4     5 

79  I8976 

8982 

89878993 

8998 

9004 

9009 

9015 

9020  9025 

233 

4     5 

80  19031 

9036 

9042  9047 

9053 

9058 

9063 

9069 

9074 

9°  79 

233 

445 

81    9085 

9090 

9096  9101 

9106 

9112 

9117 

9122  9128 

9!33 

233 

445 

82 

9138 

9143 

9149  9154 

9*59 

9*65 

9170 

9175  9i8o 

9.86 

233 

445 

83 

9191 

9196 

9201  9206 

9212 

9217 

9222 

9227  9232 

9238 

233 

445 

84 

9243 

9248 

9253  9258 

)263 

9269 

9274 

9279 

9284 

9280 

233 

445 

85 

9294 

9299 

9304  9309 

9315 

9320 

9325 

9330 

9335 

934" 

233 

445 

86 

9345 

9350 

9355  936o 

9365 

737° 

9375 

9380 

9385 

9390 

233 

445 

87 

9395 

9400 

9405  9410 

9415 

9420 

9425 

9430 

9435 

9440 

2           3 

344 

88 

9445 

945° 

9455  946o 

9465 

9469 

9474 

9479 

9484 

9489 

2           3 

344 

89 

9494 

499 

9504  9509 

9513 

95i8 

9523 

9528 

9533 

9538 

»          3 

344 

90 
91 

9542 
959° 

9547 
9595 

9552  9557 
9600  9605 

9562 
9609 

9566 
9614 

9571 
9619 

9576 
9624 

$8 

9586 
9633 

2           3 
2           3 

344 

344 

92 

9638 

9643 

9647  9652 

9657 

9661 

9666 

9671 

9675 

9680 

2           3 

344 

93 

9685 

9689 

9694  9699 

9703 

9708 

9713 

9717 

9722 

9727 

2           3 

344 

94 

973  i 

9736 

974^9745 

9750 

9754 

9759 

9763 

9768 

9773 

2           3 

344 

95 

9777 

9782 

9786^791 

9795 

9800 

9805 

9809 

9814 

9818 

2           3 

344 

96 
97 

9823 
9868 

9827 
9872 

9832  9836 
98779881 

9841 
9886 

9845 
9890 

9850 
9894 

9854 
9899 

9859 
9903 

9863 
9908 

2           3 

2           3 

344 
344 

98 

9912 

9917 

9921  9926 

9930 

9934 

9939 

9943  9948 

9952 

2           3 

344 

99 

9956 

9961 

9965  9969 

9974 

9978 

9983 

9987999' 

9996 

2           3 

334 

INDEX. 


Air,  properties  of,  100 
Air-compressor,  135 
Air-pump,  137 
Brumbo  pulley,  32 
Clearance,  97 
Combined  diagrams,  128 
Compound  engines,  123 
Cord  and  knots,  26,  28,  40 
Density,  99 

Diagrams,  oscillations  in,  118 
Diesel  motor,  140 
Drum- detent,  28 
Electrical  attachment,  30 
Engine  constant,  95 
Errors  of  indicator,  46 
Gas-engines,  140 
Gases,  properties  of,  100 
Horse-power,  92 
Hyperbola,  114 
Indicator,  Bachelder,  15 

Crosby,  5 

Tabor,  13 

Thompson,  IO 

Watt,  i 

Indicator,  care  of,  42 
Indicator  cock,  20 
Indicator  diagram,  43 
Indicator  for  gas-engines,  15 
Indicator  for  ordnance,  18 


Indicator- tester,  57 
Inspection  of  indicator,  22 
Mean  effective  pressure,  63,  81 
Pantagraph,  54 
Paper  for  indicator,  25 
Piping,  effect  of,  62 
Piston-friction,  120 
Piston-displacement,  95 
Plammeter,  Amsler,  70 

Coffin,  83 

Lippincott,  Willis,  85 
Pressure,  specific,  99 
Pump  diagrams,  131 
Reducing  motions,  32 
Reducing  wheel,  38 
Refrigerating  machine,  141 
Scale  of  spring,  42,  54 
Steam-consumption,  103 
Steam  per  horse-power,  no 
Steam,  properties  of,  102 
Swinging  lever,  37 
Taking  diagrams,  41 
Temperature,  99 
Thermal  unit,  112 
Thermal  units  per  horse-power,  112 
Three-way  cock,  21 
Valve-setting,  121 
Volume,  specific,  100 

153 


•e 


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STAMPED  BELOW 


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WILL  BE  ASSESSED  FOR  FAILURE  TO  RETURN 
THIS  BOOK  ON  THE  DATE  DUE.  THE  PENALTY 
WILL  INCREASE  TO  SO  CENTS  ON  THE  FOURTH 
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OCT  26  1933 


QCT 


359953 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


>*&:* 


